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Wikipedia

Ambigram

February 27, 2023

An ambigram is a calligraphic design that has several interpretations as written.[2]

Ambigram of the word ambigram. 180° rotational symmetry.[1]

The term was coined by Douglas Hofstadter in 1983. Most often, ambigrams appear as visually symmetrical words. When flipped, they remain unchanged, or they mutate to reveal another meaning. "Half-turn" ambigrams undergo a point reflection (180° rotational symmetry) and can be read upside down, mirror ambigrams have an axial symmetry and can be read through a reflective surface (like a mirror or a mirroring lake), and many other types of ambigrams exist.

Ambigrams are found in different languages, various alphabets and the notion often extends to numbers and other symbols. It is a recent interdisciplinary concept, combining art, literature, mathematics, cognition, and optical illusions. Drawing symmetrical words constitutes also a recreational activity for amateurs. Numerous ambigram logos are famous, and ambigram tattoos have become increasingly popular. There are methods to design an ambigram, a field in which some artists have become specialists.

Etymology

The word ambigram was coined in 1983 by Douglas Hofstadter, an American scholar of cognitive science best known as the Pulitzer Prize-winning author of the book Gödel, Escher, Bach.[3][2][4]

Hofstadter describes ambigrams as "calligraphic designs that manage to squeeze in two different readings."[5] "The essence is imbuing a single written form with ambiguity".[6]

An ambigram is a visual pun of a special kind: a calligraphic design having two or more (clear) interpretations as written words. One can voluntarily jump back and forth between the rival readings usually by shifting one's physical point of view (moving the design in some way) but sometimes by simply altering one's perceptual bias towards a design (clicking an internal mental switch, so to speak). Sometimes the readings will say identical things, sometimes they will say different things.[2]

— Douglas Hofstadter

Hofstadter attributed the origin of the word ambigram to conversations among a small group of friends during 1983–1984.[4]

Prior to Hofstadter's terminology, other names were used to refer to ambigrams. Among them, the expressions "vertical palindromes" by Dmitri Borgmann[7] (1965) and Georges Perec,[8][9] "designatures" (1979),[10] "inversions" (1980) by Scott Kim,[11][12] or simply "upside-down words" by John Langdon and Robert Petrick.[12]

Ambigram was added to the Oxford English Dictionary in March 2011,[13] and to the Merriam-Webster dictionary in September 2020.[14][15]Scrabble included the word in its database in November 2022.[16][17][18]

History

 
Sator square (word square and palindrome) with the letters S and N reversed.
 
Rotational ambigram Puzzle / The end by Peter Newell designed in 1893.
 
Mirror ambigram ΝΙΨΟΝ ΑΝΟΜΗΜΑΤΑ ΜΗ ΜΟΝΑΝ ΟΨΙΝ (Wash your sins, not only your face, in Ancient Greek) in the church Hagia Sophia (Turkey).[19]
 
Ambigrams published in The Strand Magazine, June 1908.

Many ambigrams can be described as graphic palindromes.

The first Sator square palindrome was found in the ruins of Pompeii, meaning it was created before the Eruption of Mount Vesuvius in 79 AD. A sator square using the mirror writing for the representation of the letters S and N was carved in a stone wall in Oppède (France) between the Roman Empire and the Middle Ages,[20] thus producing a work made up of 25 letters and 8 different characters, 3 naturally symmetrical (A, T, O), 3 others decipherable from left to right (R, P, E), and 2 others from right to left (S, N). This engraving is therefore readable in four directions.[21]

Although the term is recent, the existence of mirror ambigrams has been attested since at least the first millennium. They are generally palindromes stylized to be visually symmetrical.

In ancient Greek, the phrase "ΝΙΨΟΝ ΑΝΟΜΗΜΑΤΑ ΜΗ ΜΟΝΑΝ ΟΨΙΝ" (wash the sins, not only the face), is a palindrome found in several locations, including the site of the church Hagia Sophia in Turkey.[19][22] It is sometimes turned into a mirror ambigram when written in capital letters with the removal of spaces, and the stylization of the letter Ν (Ν).

A boustrophedon is a type of bi-directional text, mostly seen in ancient manuscripts and other inscriptions. Every other line of writing is flipped or reversed, with reversed letters. Rather than going left-to-right as in modern European languages, or right-to-left as in Arabic and Hebrew, alternate lines in boustrophedon must be read in opposite directions. Also, the individual characters are reversed, or mirrored. This two-way writing system reveals that modern ambigrams can have quite ancient origins, with an intuitive component in some minds.

Mirror writing in Islamic calligraphy flourished during the early modern period, but its origins may stretch as far back as pre-Islamic mirror-image rock inscriptions in the Hejaz.[23]

The earliest known non-natural rotational ambigram dates to 1893 by artist Peter Newell.[24] Although better known for his children's books and illustrations for Mark Twain and Lewis Carroll, he published two books of reversible illustrations, in which the picture turns into a different image entirely when flipped upside down. The last page in his book Topsys & Turvys contains the phrase The end, which, when inverted, reads Puzzle. In Topsys & Turvys Number 2 (1902), Newell ended with a variation on the ambigram in which The end changes into Puzzle 2.

In March 1904 the Dutch-American comic artist Gustave Verbeek used ambigrams in three consecutive strips of The UpsideDowns of old man Muffaroo and little lady Lovekins.[25] His comics were ambiguous images, made in such a way that one could read the six-panel comic, flip the book and keep reading.

From June to September 1908, the British monthly The Strand Magazine published a series of ambigrams by different people in its "Curiosities" column.[26] Of particular interest is the fact that all four of the people submitting ambigrams believed them to be a rare property of particular words. Mitchell T. Lavin, whose "chump" was published in June, wrote, "I think it is in the only word in the English language which has this peculiarity," while Clarence Williams wrote, about his "Bet" ambigram, "Possibly B is the only letter of the alphabet that will produce such an interesting anomaly."[26][27]

Characteristics

Natural ambigrams

 
The distress signal SOS is a natural rotating ambigram.
 
OHIO, a "quarter-turn" natural ambigram
 
The number 619 constitutes a natural ambigram (but not the word "western").

In the Latin alphabet, many letters are symmetrical glyphs. Most obviously the letter O. The capital letters B, C, D, E, H, I, K, O, and X have a horizontal symmetry axis. This means that all words that can be written using only these letters are natural lake reflection ambigrams. For example, BOOK, CHOICE, or DECIDE.

The lowercase letters l, o, s, x and z are rotationally symmetrical, while pairs such as b/q, d/p, m/w, n/u, and in some typefaces h/y and a/e, are rotations of each other. Thus, the words "sos", "pod", "suns", "yeah, "swims", "dollop", or "passed" form natural rotational ambigrams.

More generally, a "natural ambigram" is a word that possesses one or more symmetries when written in its natural state, requiring no typographic styling. The words "bud", "bid", or "mom", form natural mirror ambigrams when reflected over a vertical axis, as does "ليبيا", the name of the country Libya in Arabic. The words "HIM", "TOY, "TOOTH" or "MAXIMUM", in all capitals, form natural mirror ambigrams when their letters are stacked vertically and reflected over a vertical axis. The uppercase word "OHIO" can flip a quarter to produce a 90° rotational ambigram when written in serif style (with large "feet" above and below the "I").

Like all strobogrammatic numbers, 69 is a natural rotational ambigram.

Patterns in nature are visible regularities of form found in the natural world.[28] Similarly, patterns in ambigrams are regularities found in graphemes. As a consequence to this "natural" property, some shapes appear more or less appropriate to handle for the designer. Ambigram candidates can become "almost natural", when all the letters except maybe one or two are symmetrically cooperative, for example the word "awesome" possesses 5 compatible letters (the central s that flips around itself, and the couples a/e and w/m).

Single words or several words

A symmetrical ambigram can be called "homogram" (contraction of "homo-ambigram") when it remains unchanged after reflection, and "heterogram" when it transforms.[29][30] In the most common type of ambigram, the two interpretations arise when the image is rotated 180 degrees with respect to each other (in other words, a second reading is obtained from the first by simply rotating the sheet).

Single word ambigrams

Douglas Hofstadter coined the word "homogram" to define an ambigram with identical letters.[29][30] In this case, the first half of the word turns into the last half.[12]

Several words

 
Three words ambigram: a changing combination "India / Nepal" associated with the invariant conjunction "and".

A symmetrical ambigram is called "heterogram"[29][30] (contraction of "hetero-ambigram") when it gives another word. Visually, a heterogram ambigram is symmetrical only when both versions of the pairing are shown together. The aesthetical appearance is more difficult to design, when a changing ambigram aims to be revealed in one way only, alternatively or separately, because symmetry generally enhances elegance. Technically, there are twice more combinations of letters involved in a hetero-ambigram than in a homo-ambigram. For example, the 180° rotational ambigram "yeah" contains only two pairs of letters: y/h and e/a, whereas the heterogram "yeah / good" contains four : y/d, e/o, a/o, and h/g.

A single word ambigram cannot be hetero-, but a multiple words ambigram can be homo- type if the letters overlapse, like in "upsidedown" written attached, for example. The ambigram saying "upsidedown" one way and "upsidedown" again the other way, means it is a two words homogram. But the ambigram saying "upside" one way and "down" after rotation, means it is a two words heterogram.

There is no limitation to the number of words potentially associable, and full ambigram sentences have even been published.[8][12]

  •  

    "Ambigram / Wikipedia", hetero- type.[31]

  •  

    "True flag", self-referential flag, horizontal axis mirror hetero- type.

  •  

    Two words ambigram "Stay Here".

  •  

    Two words ambigram "Real / Fake" showing alternatively one version of the pair.

Types

Ambigrams are exercises in graphic design that play with optical illusions, symmetry and visual perception. Some ambigrams feature a relationship between their form and their content. Ambigrams usually fall into one of several categories.

180° rotational ambigrams

 
180° rotational ambigram saying "Upside Down".[32]

"Half-turn" ambigrams or point reflection ambigrams, commonly called "upside-down words", are 180° rotational symmetrical calligraphies.[3] We can read them right side up or upside down, or both.

Rotation ambigrams are the most common type of ambigrams for good reason. When a word is turned upside down, the top halves of the letters turn into the bottom halves. And because our eyes pay attention primarily to the top halves of letters when we read, that means that you can essentially chop off the top half of a word, turn it upside down, and glue it to itself to make an ambigram. [...][12]

— Scott Kim
  •  

    Rotating ambigram "Say Yes", half-turn type with 8 occurrences of the same pattern.

  •  

    Point reflection ambigram merci.

  •  

    "Home / Away", 180° rotational hetero-ambigram.

  •  

    "Lift", half-turn ambigram logo.

Mirror ambigrams

A mirror ambigram, or reflection ambigram, is a design that can be read when reflected in a mirror vertically, horizontally, or at 45 degrees,[12] giving either the same word or another word or phrase.

Vertical axis reflection ambigrams

 
Vertical axis reflection ambigram "Love you", with the letter I added over like in a totem ambigram.
 
"Perfect", vertical axis mirror ambigram.
 
"Nothing written", self-referential visual wordplay, vertical axis reflection.
 
Historical Maoam logo (candy), vertical axis mirror ambigram, between 1900 and 1931.

When the reflecting surface is vertical (like a mirror for example), the calligraphic design is a vertical axis mirror ambigram.

The "museum" ambigram is almost natural with mirror symmetry, because the first two letters are easily exchanged with the last two, and the lowercase letter e can be transformed into s by a fairly obvious typographical acrobatics.[33]

Vertical axis mirror ambigrams find clever applications in mirror writing (or specular writing), that is formed by writing in the direction that is the reverse of the natural way for a given language, such that the result is the mirror image of normal writing: it appears normal when it is reflected in a mirror. For example, the word "ambulance" could be read frontward and backward in a vertical axis reflective ambigram. Following this idea, the French artist Patrice Hamel created a mirror ambigram saying "entrée" (entrance, in French) one way, and "sortie" (exit) the other way, displayed in the giant glass façade of the Gare du Nord in Paris, so that the travelers coming in read entrance, and those leaving read way out.[34]

Horizontal axis reflection ambigrams

 
"Motel" on the facade of a building is mirroring in the water of a pond to give "Water", self-referential concept using a lake reflection.
 
Horizontal axis mirror ambigram "Body / Yoga".

When the reflecting surface is horizontal (like a mirroring lake for example), the calligraphic design is a horizontal axis mirror ambigram.

The book Ambigrams Revealed features several creations of this type, like the word "Failure" mirroring in the water of a pond to give "Success", or "Love" changing into "Lust".[12]

Figure-ground ambigrams

 
Figure-ground ambigram Michel Onfray, revealing the surname in the negative space formed by the letters of the given name.
 
Figure-ground ambigram "Wow / Mom" (and incidentally also a tessellation and a 180° rotational ambigram).

In a figure / ground ambigram, letters fit together so the negative space around and between one word spells another word.[12]

In Gestalt psychology, figure–ground perception is known as identifying a figure from the background. For example, black words on a printed paper are seen as the "figure", and the white sheet as the "background". In ambigrams, the typographic space of the background is used as negative space to form new letters and new words. For example, inside a capital H, one can easily insert a lowercase i.

The oil painting You & Me (US) by John Langdon (1996) belongs to this category. The word "me" fills the space between the letters of "you".[35]

Ambigram tessellations

 
Ambigram tessellation "Future", 180° rotational symmetry. Upside-down, the light-color letters "future" occupy the negative space between the dark color letters. Two tints, blue and black, separate each block.

With Escher-like tessellations associated to word patterns, ambigrams can be oriented in three, four, and up to six directions via rotational symmetries of 120°, 90° and 60° respectively,[36] such as those created by French artist Alain Nicolas.[37] Some words can also transform in the negative space, but the multiplication of constraints often has the effect of reducing either the readability or the complexity of the designed words.

Ambigram tessellations are sorts of word puzzles, in which geometry set the rules.[37]

Chain ambigrams

 
Chain ambigram Michel Onfray.
 
This chain ambigram "nouvel an" (new year, in French) reads upside down.

A chain ambigram is a design where a word (or sometimes words) are interlinked, forming a repeating chain.[12] Letters are usually overlapped: a word will start partway through another word. Sometimes chain ambigrams are presented in the form of a circle. For example, the chain "...sunsunsunsun..." can flip upside down, but not the word "sun" alone, written horizontally. A chain ambigram can be constituted of one to several elements. A single element ambigram chain is like a snake eating its own tail. A two-elements ambigram chain is like a snake eating the neighbor's tail with the neighbor eating the first snake's, and so on.

Scott Kim's "Infinity" works, and that of John Langdon "Chain reaction", are also self-referential, since the first is infinite in the literal sense of the word, and the second, both reversible at 180° and interfering around the letter O, evokes a chain reaction.[12]

Spinonyms

A spinonym [de] is a type of ambigram in which a word is written using the same glyph repeated in different orientations.[12] WEB is an example of a word that can easily be made into a spinonym.

  •  

    MBE [it] (Motor Bike Expo) spinonym logo. The same glyph is repeated in three different orientations.

  •  

    Spinonym "neun 9" (German for nine), five times the same glyph repeated in different orientations.

  •  

    "Happy new year" spinonym, the same glyph in different orientations shapes the twelve letters of the sentence.

Perceptual shift ambigrams

 
Perceptual shift ambigram, Wave and Particle, by Douglas Hofstadter.
 
Ambiguous letter that can be interpreted as a H or as an A.

Perceptual shift ambigrams, also called "oscillation" ambigrams, are designs with no symmetry but can be read as two different words depending on how the curves of the letters are interpreted.[12] These ambigrams work on the principle of rabbit-duck-style ambiguous images.

For example Douglas Hofstadter expresses the dual nature of light as revealed by physics with his perceptual shift ambigram Wave / Particle.

90° rotational ambigrams

 
"Ignore Wrong!", also "Wrong! / Ignore", 90° rotational symmetry.
 
90° rotational ambigram "Jude / Muslim" (Jew / Muslim in German) (and incidentally also a chain ambigram).

"Quarter-turn" ambigrams or 90° rotational ambigrams turn clockwise or counterclockwise to express different meanings.[2] For example, the letter U can turn into a C and reciprocally, or the letters M or W into an E.[12]

Totem ambigrams

 
This historical Maria monogram is close to a totem ambigram, almost symmetrical over the vertical axis.
 
The Alabama A&M University has a totem mirror ambigram logo.
 
Words crossing or totem ambigram "Hot dog", vertical axis reflection symmetry.

A totem ambigram is an ambigram whose letters are stacked like a totem, most often offering a vertical axis mirror symmetry. This type helps when several letters fit together, but hardly the whole word. For example, in the Maria monogram [hu], the letters M, A and I are individually symmetrical, and the pairing R/A is almost naturally mirroring. When adequately stacked, the 5 letters produce a nice totem ambigram, whereas the whole name "Maria" would not offer the same cooperativeness.

The ambigrammist artist John Langdon designed several totemic assemblages, such as the word "METRO" composed of the symmetrical letter M, then section ETR, and below O; or the sentence "THANK YOU", vertical assembly of T, H, A, then of the symmetric NK couple, then finally Y, O, U.[38]

Fractal ambigrams

In mathematics, a fractal is a geometrical shape that exhibits invariance under scaling. A piece of the whole, if enlarged, has the same geometrical features as the entire object itself. A fractal ambigram is a sort of space-filling ambigrams where the tiled word branches from itself and then shrinks in a self-similar manner, forming a fractal.[39] In general, only a few letters are constrainted in a fractal ambigram. The other letters don't need to look like any other, and thus can be shaped freely.

3-Dimensional ambigrams

 
The 3D ambigram "GEB" (for Gödel, Escher, Bach) on the cover of Hofstadter's book.
 
Three-dimensional ambigram, ABC.

A 3D ambigram is a design where an object is presented that will appear to read several letters or words when viewed from different angles. Such designs can be generated using constructive solid geometry, a technique used in solid modeling, and then physically constructed with the rapid prototyping method.

3-dimensional ambigram sculptures can also be achieved in plastic arts. They are volume ambigrams.

The original 1979 edition of Hofstadter's Gödel, Escher, Bach featured two 3-D ambigrams on the cover.[40]

Complex ambigrams

Complex ambigrams are ambigrams involving more than one symmetry, or satisfying the criteria for several types. For example, a complex ambigram can be both rotational and mirror with a 4-fold dihedral symmetry. Or a spinonym that reads upside down is also a complex ambigram.

Symbols

Other languages

 
Mirror ambigram depicting the phrase علي ولي الله (Ali is the vicegerent of God, in Arabic), Ottoman panel, between 1720 and 1730.
 
Ambigram 곰 / 문 (Bear / Door, in Korean), 180° rotational symmetry.
 
The word "বাংলা" (Bangla or Bengali, in Bengali), half-turn ambigram.

Ambigrams exist in many languages. With the Latin alphabet, they generally mix lowercase and uppercase letters. But words can also be symmetrical in other alphabets, like Arabic, Bengali, Cyrillic, Greek, and even in Chinese characters and Japanese kanji.

In Korean, 곰 (bear) and 문 (door), 공 (ball) and 운 (luck), or 물 (water) and 롬 (ROM) form a natural rotational ambigram. Some syllables like 응 (yes), 표 (ticket/signage) or 를 (object particle), and words like "허리피라우" (straighten your back) also make full ambigrams.

The han character meaning "hundred" is written 百, that makes a natural 90° rotational ambigram when the glyph makes a quarter turn counterclockwise, one sees "100".[41]

  Media related to Ambigrams by language at Wikimedia Commons.

Numbers

 
Mirror and rotational ambigram of an arithmetic operation illustrating the commutative property in addition.[32]
 
Although not totally symmetrical, the Sochi 2014 (Olympic games) official logo offers mirror and rotational symmetries, linking the numbers to the letters like an ambigram.
 
Rio 2016 (Olympic games), half-turn rotational ambigram logo containing letters and digits.

An ambigram of numbers, or numeral ambigram, contains numerical digits, like 1, 2, 3...[12]

In mathematics, a palindromic number (also known as a numeral palindrome) is a number that remains the same when its digits are reversed through a vertical axis (but not necessarily visually). The palindromic numbers containing only 1, 8, and 0, constitute natural numeric ambigrams (visually symmetrical through a mirror). Also, because the glyph 2 is graphically the mirror image of 5, it means numbers like 205 or 85128 are natural numeral mirror ambigrams. Though not palindromic in the mathematical sense, they read frontward and backward like real ambigrams.

A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated 180 degrees. The numeral looks the same right-side up and upside down (e.g., 69, 96, 1001).[42][43][44]

Some dates are natural numeral ambigrams.[45] In March 1961, artist Norman Mingo created an upside-down cover for Mad magazine featuring an ambigram of the current year. The title says "No matter how you look at it... it's gonna be a Mad year. 1961, the first upside-down year since 1881."[46] Tuesday, 22 February 2022, was a palindrome and ambigram date called "Twosday" because it contained reversible 2 (two).[47][48][49]

Ambigrams of numbers receive most attention in the realm of recreational mathematics.[2][50]

Ambigrams with numbers sometimes combine letters and numerical digits. Because the number 5 is approximately shaped like the letter S, the number 6 like a lowercase b, the number 9 like the letter g, it is possible to play on these similarities to design ambigrams. A good example is the Sochi 2014 (Olympic games) logo where the four glyphs contained in 2014 are exact symmetries of the four letters S, o, i and h, individually.[51]

Other symbols

 
Palindrome with musical notes, here the centre part of Alban Berg's opera Lulu

As alphabet letters are glyphs used in the writing systems to express the languages visually, other symbols are also used in the world to code other fields, like the prosigns in the Morse code or the musical notes in music.

Similarly to the ambigrams of letters, the ambigrams with other symbols are generally visually symmetrical, either point reflective or reflective through an axis.

The international Morse code distress signal SOS   ▄ ▄ ▄ ▄▄▄ ▄▄▄ ▄▄▄ ▄ ▄ ▄  is a natural ambigram constituted of dots and dashes. It flips upside down or through a mirror.

In morse code, the letter P coded   ▄ ▄▄▄ ▄▄▄ ▄  and the letter R coded   ▄ ▄▄▄ ▄  are individually symmetrical, like many other letters and numbers. Also, the letter G coded   ▄▄▄ ▄▄▄ ▄  is the exact reverse of the letter W coded   ▄ ▄▄▄ ▄▄▄ . Thus, the combination   ▄▄▄ ▄▄▄ ▄  /   ▄ ▄▄▄ ▄▄▄  coding the pairing G/W constitutes a natural ambigram. Consequently, meaningful natural ambigrams written in morse code certainly exist, like for example the words "wog"   ▄ ▄▄▄ ▄▄▄   ▄▄▄ ▄▄▄ ▄▄▄    ▄▄▄ ▄▄▄ ▄ , "Dou"   ▄▄▄ ▄ ▄    ▄▄▄ ▄▄▄ ▄▄▄    ▄ ▄ ▄▄▄  or "mom"   ▄▄▄ ▄▄▄    ▄▄▄ ▄▄▄ ▄▄▄    ▄▄▄ ▄▄▄ .[3][52][53]

In music, the interlude from Alban Berg's opera Lulu is a palindrome, thus the score made up of musical notes is almost symmetrical through a vertical axis.[54]

In biology, researchers study the ambigrammatic property of narnaviruses by using visual representations of the symmetrical sequences.[28][1][55]

Fields

Art

Calligraphy and typography

 
Ambigram Love Song published in a typography book (Typism).
 
Calligraphic color-reversal ambigram Soul of Laos, published in the book Ambigrams Revealed.[12]
 
Calligraphic design Danke (thanks, in German) and half-turn ambigram.

Instead of simply writing them, ambigram lettering covers the art of drawing letters. In ambigram calligraphy, each letter acts as an illustration, each letter is created with attention to detail and has a unique role within a composition. Lettering ambigrams do not translate into combinations of alphabet letters that can be used like a typeface, since they are created with a specific candidate in mind.

The calligrapher, graffiti writer and graphic designer Niels Shoe Meulman created several rotational ambigrams like the number "fifty",[12] the names "Shoe / Patta",[12] and the opposition "Love / Fear".[56]

The cover of the 7th volume of the typography book Typism is an ambigram drawn by Nikita Prokhorov.[57]

The American type designer Mark Simonson designed poetic and humorous ambigrams, such as the words "Revelation", "Typophile", and the symbiosis "Drink / Drunk".[12] The last one makes a visual pun when printed on a shot glass, sold commercially.[58]

Logos

 
The rotational logo New Man created by Raymond Loewy in 1968 is a natural ambigram.
 
The online two-sided marketplace for residential cleaning Handy has a 180° rotational ambigram logo.
 
Sun (Microsystems) logo designed by Vaughan Pratt in 1982, chain ambigram, spinonym, 90° and 180° rotational symmetries.
 
Nissin (Foods) ambigram visual identity (half-turn).

Since they are visually striking, and sometimes surprising, ambigram words find large application in corporate logos and wordmarks, setting the visual identity of many organizations, trademarks and brands.[59]

In 1968[60] or 1969, Raymond Loewy designed the rotational New Man [fr] ambigram logo.[61][62][63]

The mirror ambigram DeLorean Motor Company logo, designed by Phil Gibbon, was first used in 1975.[64][65][66]

Robert Petrick designed the invertible Angel logo[12] in 1976.

The logo Sun (Microsystems) designed by professor Vaughan Pratt[67] in 1982 fulfills the criteria of several types: chain ambigram, spinonym, 90° and 180° rotational symmetries.

The Swedish pop group ABBA owns a mirror ambigram logo stylized AᗺBA with a reversed B, designed by Rune Söderqvist [sv][68] in 1976.[69]

The Ventura logo of the Visitors & Convention Bureau's board, in California, cost US$25,000 and was created in 2014 by the DuPuis group. It uses a 180° rotational symmetry.[70][71]

Other famous ambigram logos include: the insurance company Aviva;[72] the acronym CRD (Capital Regional District) in the Canadian province of British Columbia;[73] the American multinational corporation DXC Technology; the two-sided marketplace for residential cleaning Handy;[74][75] the brand name of French premium high-speed train services InOui;[76] the French company specializing in ticketing and passenger information systems IXXI; the century-old brand Maoam of the confectionery manufacturer Haribo;[77] the American industrial rock band NIͶ; the Japanese food company Nissin; the biotechnology company Noxxon Pharma, founded in 1997; the online travel agency Opodo in 2001;[78] the brand of food products OXO[79] born in 1899; the video game Pod; the American developer and manufacturer of audio products Sonos;[80] the American professional basketball team Phoenix Suns;[81][82] the German manufacturer of adhesive products UHU; the quadruple symmetrical logo UA from the American clothing brand Under Armour ; the Canadian corporation mandated to operate intercity passenger rail service VIA in 1978;[83] the American international broadcaster VOA, born in 1942; and the Malaysian mobile virtual network operator XOX. The student edition of the Tesco Clubcard used 180° rotational symmetry.[84]

Visual communication

 
Ambigram "Biden USA Harris" by Douglas Hofstadter conveying a political message during the 2020 United States presidential election.
 
The movie Anna by Luc Besson (2019) reveals on its poster a mirror ambigram with a vertical axis.

Because they are visual puns,[2] ambigrams generally attract attention, and thus can be used in visual communication to broadcast a marketing or political message.

In France, a mirror ambigram "Penelope / benevole" legible through a horizontal axis became a meme on the web after its diffusion on Wikimedia Commons.[85]Penelope Fillon, wife of French politician and former Prime Minister of France François Fillon, is suspected of having received wages for a fictitious job. Ironically, her name through the mirror becomes benevole (voluntary in French), suggesting dedication for a free service. Shared tens of thousands of times on the social networks, this humorous ambigram made the buzz via several French,[86] Belgian[87][88] and Swiss[85] medias.

Ambigrams are regularly used by communication agencies such as Publicis to engage the reader or the consumer through two-way messages.[89] Thus, in 2021, male first names transformed into female first names are included in a Swiss advertising campaign aimed at raising awareness about gender equality. An intriguing catchphrase typography upside down invites the reader to rotate the magazine, in which the first names "Michael" or "Peter" are transformed into "Nathalie" or "Alice".[90][91]

In 2015 iSmart's logo on one of its travel chargers went viral because the brand's name turned out to be a natural ambigram that read "+Jews!" upside down. The company noted that "...we learned a powerful lesson of what not to do when creating a logo." [92]

Cinema posters sometimes seduce observers with ambigram titles, such as that of Tenet by Christopher Nolan, by central symmetry.[21] or Anna by Luc Besson around a vertical axis,[93][94]

Comics

 
Ambigrams in comics by Gustave Verbeek in 1904.
 
Ambigrams in comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo by Gustave Verbeek containing ambigram sentences in 1904.
 
Another frame.

The American artist and writer Peter Newell published a rotational ambigram in 1893 saying "Puzzle / The end" in the book containing reversible illustrations Topsys & Turvys.[24]

In March 1904 the Dutch-American comic artist Gustave Verbeek used ambigrams in three consecutive strips of The UpsideDowns of old man Muffaroo and little lady Lovekins.[25] His comics were ambiguous images, made in such a way that one could read the six-panel comic, flip the book and keep reading. In The Wonderful Cure of the Waterfall (13 March 1904) an Indian medicine man says 'Big waters would make her very sound', while when flipped the medicine man turns into an Indian woman who says 'punos dery, eay apew poom, serlem big'. Which is explained as, 'poor deary' several foreign words that meant that she would call the 'Serlem Big'. The next comic called At the House of the Writing Pig (20 March 1904), where two ambigram word balloons are featured. The first features an angry pig trying to make the main protagonist leave by showing a sign that says; 'big boy go away, dis am home of mr h hog', up side down it reads 'Boy yew go away. We sip. Home of hog pig.' The protagonist asks the pig if it wants a big bun, upon which it replies 'Why big buns? Am mad u!', which flips into 'In pew we sang big hym'. Finally in The Bad Snake and the Good Wizard (1904 Mar 27) there are two more ambigrams. The first turns 'How do you do' into the name of a wizard called 'Opnohop Moy', the second features a squirrel telling the protagonist 'Yes further on' only to inform it that there are 'No serpents here' on his way back. In a 2012 Swedish remake of the book,[95] the artist Marcus Ivarsson redraws The Bad Snake and the Good Wizard in his own style. He removes the squirrel, but keeps the other ambigram. 'How do you do' is replaced by 'Nejnej' (Swedish for no) and the wizard is now called 'Laulau'.

  Media related to Ambigrams by Gustave Verbeek at Wikimedia Commons.

Oubapo, workshop of potential comic book art, is a comics movement which believes in the use of formal constraints to push the boundaries of the medium. Étienne Lécroart, cartoonist, is a founder and key member of Oubapo association, and has composed cartoons that could be read either horizontally, vertically, or in diagonal, and vice versa, sometimes including appropriate ambigrams.[96]

Drawings and paintings

 
Ambigram "¡OHO!" published by Rex Whistler in 1946.
 
Ambigram "¡OHO!" with reversible faces by Rex Whistler created before 1944. A young woman transforms into a grandmother.
 
Ambigram painting Me / We, horizontal axis mirror type (2007).

The British painter, designer and illustrator Rex Whistler, published in 1946 a rotational ambigram "¡OHO!" for the cover of a book gathering reversible drawings.[97]

The artist John Langdon, specialist of ambigrams,[59] designed many color paintings featuring ambigrams of all kinds, figure-ground, rotational, mirror or totem. Among other influences, he particularly admires M. C. Escher's drawings.[12]

The Canadian artist Kelly Klages painted several acrylics on canvas with ambigram words and sentences referring to famous writers' novels written by William Shakespeare or Agatha Christie, such as Third Girl, The Tempest, After the Funeral, The Hollow, Reformation, Sherlock Holmes, and Elephants Can Remember.[98]

Sculptures

 
Ambigram OUI / NON (Yes / No, in French), by sculptor Markus Raetz, installed at the top of a pole on the Place du Rhöne in Geneva, Switzerland, observed from two angles.
Mia Florentine Weiss
 
"Love Hate" sculpture in Munich, Germany, in 2020.
 
"Now / Won" installation in front of the Reichstag building, Berlin, Germany, 2017.

The German conceptual artist Mia Florentine Weiss built a sculptural ambigram Love Hate [de],[99] that has traveled Europe as a symbol of peace and change of perspective.[100] Depending on which side the viewer looks at it, the sculpture says "Love" or "Hate". A similar concept was installed in front of the Reichstag building in Berlin with the words "Now / Won". Both sculptures are mirror type ambigrams, symmetrical around a vertical axis.[101]

The Swiss sculptor Markus Raetz made several three-dimensional ambigram works, featuring words generally with related meanings, such as YES-NO (2003),[102] ME-WE (2004, 2010),[103] OUI-NON (2000–2002) in French,[104][105] SI–NO (1996)[106] and TODO-NADA (1998) in Spanish[107][108] These are anamorphic works, which change in appearance depending on the angle of view of the observer. The OUI–NON ambigram is installed on the Place du Rhône, in Geneva, Switzerland, at the top of a metal pole. Physically, the letters have the appearance of iron twists. With the perspective, this work demonstrates that reality can be ambiguous.[105]

Some ambigram sculptures by the French conjurer Francis Tabary [fr] are reversible by a half-turn rotation, and can therefore be exhibited on a support in two different ways.[109][110]

Literature

Palindromes

 
Famous palindrome sentence "Dogma I am God" turned into a mirror ambigram. The capital D at the left was changed into a lowercase d, and the typographic spaces adjusted.
 
Georges Perec's "vertical palindrome" (rotational ambigram), in French.

Ambigrams are sorts of visual palindromes.[111] Some words turn upside down, others are symmetrical through a mirror. Natural ambigram palindromes exist, like the words "wow", "malayalam"[112] (Dravidian language), or the biotechnology company Noxxon that possesses a palindromic name associated to a rotational ambigram logo. But some words are natural ambigrams, though not palindromes in the literary acception, like "bud" for example, because b and d are different letters. As a result, some words and sentences are good candidates for ambigrammists, but not for palindromists, and reciprocally, since the constraint slightly differ. Authors of ambigrams also benefit from a certain flexibility by playing on the typeface and graphical adjustments to influence the reading of their visual palindromes.

Oulipo, workshop of potential literature, seeks to create works using constrained writing techniques. Georges Perec, French novelist and member of the Oulipo group, designed a rotational ambigram, that he called "vertical palindrome".[8] Sibylline, the sentence "Andin Basnoda a une épouse qui pue" in French means "Andin Basnoda has a smelly wife". Perec did not care about punctuation spaces, but his creation flips easily with a classical font like Arial.

Visual palindromes sometimes perfectly illustrate literary contents. The American author Dan Brown incorporated John Langdon's designs into the plot of his bestseller Angels & Demons, and his fictional character Robert Langdon's surname was a homage to the ambigram artist.[113]

The fantasy novel Abarat, written and illustrated by Clive Barker, features an ambigram of the title on its cover.[114]

Calligrams

 
Calligram "Good ambigrams" representing a face and mirror self-referential ambigram.
 
Reflective calligram hat in Alevism forming a human face with Arabic letters.
 
Oslo Climbing Club official logo[115] "OK [no]" (acronym for Oslo Klatreklubb) 90° rotational ambigram showing a human silhouette vertically.

A calligram is text arranged in such a way that it forms a thematically related image. It can be a poem, a phrase, a portion of scripture, or a single word. The visual arrangement can rely on certain use of the typeface, calligraphy or handwriting. The image created by the words illustrates the text by expressing visually what it says, or something closely associated.

In Islamic calligraphy, symmetrical calligrams appear in ancient and modern periods, forming mirror ambigrams in Arabic language.[23]

The word "OK" turned 90° counterclockwise evokes a human icon, with the letter O forming the head and the letter K the arms and the legs. The Norwegian Climbing Club Oslo Klatreklubb [no] (acronym "OK") borrowed the concept of this natural calligram for their official logo.[115]

Semantics

 
Bilingual mirror ambigram playing on the translation of the word "Lapin" (rabbit, in French).
 
Self-referential composition "here / away" displayed in a spiral to express distance, thus enhancing the meaning.

As described by Douglas Hofstadter, ambigrams are visual puns having two or more (clear) interpretations as written words.[2]

Multilingual ambigrams can be read one way in a language, and another way in a different language or alphabet.[12] Multi-lingual ambigrams can occur in all of the various types of ambigrams, with multi-lingual perceptual shift ambigrams being particularly striking.

Like certain anagrams with providential meanings such as "Listen / Silent" or "The eyes / They see", ambigrams also sometimes take on a timely sense, for example "up" becomes the abbreviation "dn", very naturally by rotation of 180°.[116] But on the other hand, it happens that the luck of the letters makes things bad. This is the case with the weird anagram "Santa / Satan", as it is with a rotational ambigram that has gone viral because of the paradoxical and unintentional message it expresses. Spotted in 2015 on a metal medal marketed without bad intention, the text "hope" displays upside down with a fairly obvious reading "Adolf", first name of the Nazi leader situated at the antipodes of optimism. This coincidence photographed by an Internet user was relayed by several media and constitutes an ambiguous image.[117][118]

Mathematics

 
Ambigram of a reversible arithmetic operation.

Recreational mathematics is carried out for entertainment rather than as a strictly research and application-based professional activity.[50] An ambigram magic square exists, with the sums of the numbers in each row, each column, and both main diagonals the same right side up and upside down (180° rotational design). Numeral ambigrams also associate with alphabet letters. A "dissection" ambigram of "squaring the circle" was achieved in a puzzle where each piece of the word "circle" fits inside a perfect square.[2]

Burkard Polster, professor of mathematics in Melbourne[119] conducted researches on ambigrams and published several books dealing with the topic, including Eye Twisters, Ambigrams & Other Visual Puzzles to Amaze and Entertain.[120] In the abstract Mathemagical Ambigrams, Polster performs several ambigrams closely related to his realm, like the words "algebra", "geometry", "math", "maths", or "mathematics".[2]

     
Message written with the digits "07734" upside down.

Calculator spelling is an unintended characteristic of the seven-segments display traditionally used by calculators, in which, when read upside-down, the digits resemble letters of the Latin alphabet. Also, palindromic numbers and strobogrammatic numbers sometimes attract attention of mathematician ambigrammists.[43][42]

Ambigram tessellations and 3D ambigrams are two types particularly fun for the mathematician in geometry. Word patterns in tessellations can start from 35 different fundamental polygons, such as the rhombus, the isosceles right triangle, or the parallelogram.[36]

Word puzzles are used as a source of entertainment, but can additionally serve an educational purpose. The American puzzle designer Scott Kim published several ambigrams in Scientific American in Martin Gardner's "Mathematical Games" column, among them long sentences like "Martin Gardner's celebration of mind" turning into "Physics, patterns and prestidigitation".[12]

Philosophy and cognition

Duality and analogy

 
Yin and yang symbol, concept of dualism.
 
"Two in one", half-turn ambigram.

In the word "ambigram", the root ambi- means "both" and is a popular prefix in a world of dualities, such as day/night, left/right, birth/death, good/evil.[12] In Wordplay: The Philosophy, Art, and Science of Ambigrams,[59] John Langdon mentions the yin and yang symbol as one of his major influences to create upside down words.

Ambigrams are mentioned in Metamagical Themas, an eclectic collection of articles that Douglas Hofstadter wrote for the popular science magazine Scientific American during the early 1980s.[6]

Seeking the balance point of analogies is an aesthetic exercise closely related to the aesthetically pleasing activity of doing ambigrams, where shapes must be concocted that are poised exactly at the midpoint between two interpretations. But seeking the balance point is far more than just aesthetic play; it probes the very core of how people perceive abstractions, and it does so without their even knowing it. It is a crucial aspect of Copycat research.[6]

— Douglas Hofstadter

Cognition and psychology

 
"Ambiguity", 180° rotational ambigram.

Legibility is an important aspect in successful ambigrams. It concerns the ease with which a reader decodes symbols. If the message is lost or difficult to perceive, an ambigram does not work.[5] Readability is related to perception, or how our brain interprets the forms we see through our eyes.[121]

Symmetry in ambigrams generally improves the visual appearance of the calligraphic words.[12] Hermann Rorschach, inventor of the Rorschach Test notices that asymmetric figures are rejected by many subjects. Symmetry supplies part of the necessary artistic composition.[122]

For many amateurs, designing ambigrams represents a recreational activity, where serendipity can play a fertile role, when the author makes an unplanned fortunate discovery.[2][26]

Magic

 
"Real world / Prank Fake", ambigram expressing illusion.
 
Ambigram "Magic / Dream", with a handheld pattern giving a reversed shadow.
 
"incredible!" Magical ambigram.[123]

In magic, ambigrams work like visual illusions, revealing an unexpected new message from a particular written word.[124]

In the first series of the British show Trick or Treat, the show's host and creator Derren Brown uses cards with rotational ambigrams.[125][126] These cards can read either 'Trick' or 'Treat'.

Ambiguous images, of which ambigrams are a part, cause ambiguity in different ways. For example, by rotational symmetry, as in the Illusion of The Cook by Giuseppe Arcimboldo (1570);[127] sometimes by a figure-ground ambivalence as in Rubin vase; by perceptual shift as in the rabbit–duck illusion, or through pareidolias; or again, by the representation of impossible objects, such as Necker cube or Penrose triangle. For all these types of images, certain ambigrams exist, and can be combined with visuals of the same type.

John Langdon designed a figure-ground ambigram "optical illusion" with the two words "optical" and "illusion", one forming the figure and the other the background. "Optical" is easier to see initially but "illusion" emerges with longer observation.[128]

Tattooing

 
Mirror ambigram tattoos on wrists "Love / Eros".
 
Handmade ambigram in tattoo "New York / Rich Man", right side up and upside down.
 
180° rotational ambigram tattoo "No religion".
 
Ambigram tattoo Texas / Sexy, 180° rotational symmetry.

One of the most dynamic sectors that harbors ambigrams is tattooing. Because they possess two ways of reading, ambigram tattoos inked on the skin benefit from a "mind-blowing" effect. On the arm, sleeve tattoos flip upside-down, on the back or jointly on two wrists they are more striking with a mirror symmetry. A large range of scripts and fonts is available. Experienced ambigram artists can create an optical illusion with a complex visual design.[129]

In 2015, an ambigram tattoo went viral following an advertising campaign developed by the Publicis group two years earlier. The Samaritans of Singapore organization, active in suicide prevention, has a 180° reversible "SOS" ambigram logo, acronym of its name and homonym of the famous SOS distress signal. In 2013, this center orders advertisements that could be inserted in magazines to make readers aware of the problem of depression among young people, and the communication agency notices the symmetrical aspect of the logo. As a result, it begins to produce several ambigrammatic visuals, staged in photographic contexts, where sentences such as "I'm fine", "I feel fantastic" or "Life is great" turn into "Save me", "I'm falling apart", and "I hate myself". Readers noticing this logo placed at the upper left corner of the page with an upside-down typographical catchphrase rotate the newspaper and visualize the double calligraphed messages, which call out with the SOS.[89][130] These ads are so influential that Bekah Miles, an American student herself coming out of a severe depression, chooses to use the "I'm fine / Save me" ambigram to get a tattoo on her thigh. Posted on Facebook, the two-sided photography immediately appeals to many young people, impressed or sensitive to this difficulty.[131][132] To educate its students, George Fox University in the United States then relays the optical illusion in its official journal, through a video totaling more than three million views[133] and the information is also reproduced in several local media and international organizations, thus helping to popularize this famous two-way tattoo.[134][135] Less fortunate, another teenage girl, aged 16, committed suicide, with her also this ambigram found on a note in her room, "I'm fine / Save me", reversible calligraphy today printed on badges and bracelets, for educational purposes.[136]

Manufacturing

Clothing and fashion

 
Ambigram "Bounce", printed inside an Adidas pink shoe.

Adidas marketed a line of sneakers called "Bounce", with an ambigram typography printed inside the shoe.

Several clothing brands, such as Helly Hansen (HH), Under Armour (UA), or New Man [fr], raise an ambigram logo as their visual identity.[63]

Mirror ambigrams are also sometimes placed on T-shirts, towels and hats, while socks are more adapted to rotational ambigrams. The conceptual artist Mia Florentine Weiss marketed T-shirts and other products with her mirror ambigram Love Hate [de].[137][100] Likewise, the city of Ventura in California sells sweatshirts, caps, jackets, and other fashion accessories printed with its rotational ambigram logo.[138]

  •  

    Rotational and reflective ambigram "Ideal", printed on a T-shirt.

  •  

    "Zen Yes" embroidered on a blue T-shirt with a meditation symmetrical pictogram.

  •  

    Helly Hansen, Norwegian manufacturer and retailer of clothing and sports equipment, has an ambigram logo.

Accessories

 
"Cognac / Danger", front and back, on a set of two shot glasses. Humorous warning related to alcohol consumption.

The CD cover of the thirteenth studio album Funeral by American rapper Lil Wayne features a 180° rotational ambigram reading "Funeral / Lil Wayne".[139]

The special edition paper sleeve (CD with DVD) of the solo album Chaos and Creation in the Backyard by Paul McCartney features an ambigram of the singer's name.[140]

The Grateful Dead have used ambigrams several times, including on their albums Aoxomoxoa and American Beauty.[citation needed]

Although the words spelled by most ambigrams are relatively short in length, one DVD cover for The Princess Bride movie creates a rotational ambigram out of two words "Princess Bride," whether viewed right side up or upside down. [141]

The cover of the studio album Create/Destroy/Create by rock band Goodnight, Sunrise is an ambigram composition constituted of two invariant words, "create" and "destroy", designed by Polish artist Daniel Dostal.[142]

The reversible shot glass containing a changing message "Drink / Drunk", created by the typographer Mark Simonson was manufactured and sold in the market.[58]

The concept of reversible sign that some merchants use through their windows to indicate that the store is sometimes "open", sometimes "closed", was inaugurated at the beginning of the 2000s, by a rotational ambigram "Open / Closed" developed by David Holst.[33]

Creating ambigrams

 
Ambigram and tessellation "Escher", handmade design.

Different ambigram artists, sometimes called ambigrammists,[6][12] may create distinctive ambigrams from the same words, differing in both style and form.

Handmade designs

There are no universal guidelines for creating ambigrams, and different ways of approaching problems coexist. A number of books suggest methods for creation, including WordPlay,[59] Eye Twisters,[120] and Ambigrams Revealed,[12] in English.

Ambigram generators

Computerized methods to automatically create ambigrams have been developed. Most of them function on the simplified principle of mapping a single letter to another single letter. Because of this weakness, most of them can only map a word to itself or to another word that is the same length and do not combine letters. Thus, the generated ambigrams are in general of poor quality when compared to hand made ambigrams. More sophisticated techniques employ databases of thousands of curves to create complex ambigrams.[citation needed] Some ambigram generators are free, while some others require payment.

Artists

John Langdon and Scott Kim each believed that they had invented ambigrams in the 1970s.[143]

Douglas Hofstadter

 
Douglas Hofstadter's mirror ambigrams featuring the names of the seven rainbow colors, followed by his signature "Doug".

Douglas Hofstadter coined the term.[2]

To explain visually the numerous types of possible ambigrams, Hofstadter created many pieces with different constraints and symmetries.[144] Hofstadter has had several exhibitions of his artwork in various university galleries.[citation needed]

According to Scott Kim, Hofstadter once created a series of 50 ambigrams on the name of all the states in the US.[12]

In 1987 a book of 200 of his ambigrams, together with a long dialogue with his alter ego Egbert G. Gebstadter on ambigrams and creativity, was published in Italy.[4]

John Langdon

John Langdon is a self-taught artist, graphic designer and painter, who started designing ambigrams in the late 1960s and early 70s. Lettering specialist, Langdon is a professor of typography and corporate identity at Drexel University in Philadelphia.[145]

John Langdon produced a mirror image logo "Starship" in 1972[146] or 1975[better source needed], that was sold to the rock band Jefferson Starship.

Langdon's ambigram book Wordplay was published in 1992. It contains about 60 ambigrams. Each design is accompanied by a brief essay that explores the word's definition, its etymology, its relationship to philosophy and science, and its use in everyday life.[59]

Ambigrams became more popular as a result of Dan Brown incorporating John Langdon's designs into the plot of his bestseller, Angels & Demons, and the DVD release of the Angels & Demons movie contains a bonus chapter called "This is an Ambigram". Langdon also produced the ambigram that was used for some versions of the book's cover.[143] Brown used the name Robert Langdon for the hero in his novels as an homage to John Langdon.[113][147]

Blacksmith Records, the music management company and record label, possesses a rotational ambigram logo[148] designed by John Langdon.[149]

Scott Kim

Scott Kim is one of the best-known masters of the art of ambigrams.[62] He is an American puzzle designer and artist who published in 1981 a book called Inversions with ambigrams of many types.[11][147]

Other artists

Nikita Prokhorov is a graphic artist, typographer and professional ambigrammist. His book Ambigrams Revealed showcases ambigram designs of all types, from all around the world.[12][150]

Born in 1946, Alain Nicolas is a specialist of figurative and ambigram tessellations. In his book, he performed many tilings with various words like "infinity", "Einstein" or "inversion" legible in many orientations.[36] According to The Guardian, Nicolas has been called "the world's finest artist of Escher-style tilings".[151]


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Further reading

External links

February 27, 2023
ambigram, ambigram, calligraphic, design, that, several, interpretations, written, word, ambigram, rotational, symmetry, term, coined, douglas, hofstadter, 1983, most, often, ambigrams, appear, visually, symmetrical, words, when, flipped, they, remain, unchang. An ambigram is a calligraphic design that has several interpretations as written 2 Ambigram of the word ambigram 180 rotational symmetry 1 The term was coined by Douglas Hofstadter in 1983 Most often ambigrams appear as visually symmetrical words When flipped they remain unchanged or they mutate to reveal another meaning Half turn ambigrams undergo a point reflection 180 rotational symmetry and can be read upside down mirror ambigrams have an axial symmetry and can be read through a reflective surface like a mirror or a mirroring lake and many other types of ambigrams exist Ambigrams are found in different languages various alphabets and the notion often extends to numbers and other symbols It is a recent interdisciplinary concept combining art literature mathematics cognition and optical illusions Drawing symmetrical words constitutes also a recreational activity for amateurs Numerous ambigram logos are famous and ambigram tattoos have become increasingly popular There are methods to design an ambigram a field in which some artists have become specialists Contents 1 Etymology 2 History 3 Characteristics 3 1 Natural ambigrams 3 2 Single words or several words 3 2 1 Single word ambigrams 3 2 2 Several words 4 Types 4 1 180 rotational ambigrams 4 2 Mirror ambigrams 4 2 1 Vertical axis reflection ambigrams 4 2 2 Horizontal axis reflection ambigrams 4 3 Figure ground ambigrams 4 4 Ambigram tessellations 4 5 Chain ambigrams 4 6 Spinonyms 4 7 Perceptual shift ambigrams 4 8 90 rotational ambigrams 4 9 Totem ambigrams 4 10 Fractal ambigrams 4 11 3 Dimensional ambigrams 4 12 Complex ambigrams 5 Symbols 5 1 Other languages 5 2 Numbers 5 3 Other symbols 6 Fields 6 1 Art 6 1 1 Calligraphy and typography 6 1 2 Logos 6 1 3 Visual communication 6 1 4 Comics 6 1 5 Drawings and paintings 6 1 6 Sculptures 6 2 Literature 6 2 1 Palindromes 6 2 2 Calligrams 6 2 3 Semantics 6 3 Mathematics 6 4 Philosophy and cognition 6 4 1 Duality and analogy 6 4 2 Cognition and psychology 6 5 Magic 6 6 Tattooing 6 7 Manufacturing 6 7 1 Clothing and fashion 6 7 2 Accessories 7 Creating ambigrams 7 1 Handmade designs 7 2 Ambigram generators 7 3 Artists 7 3 1 Douglas Hofstadter 7 3 2 John Langdon 7 3 3 Scott Kim 7 3 4 Other artists 8 References 9 Further reading 10 External linksEtymology EditThe word ambigram was coined in 1983 by Douglas Hofstadter an American scholar of cognitive science best known as the Pulitzer Prize winning author of the book Godel Escher Bach 3 2 4 Hofstadter describes ambigrams as calligraphic designs that manage to squeeze in two different readings 5 The essence is imbuing a single written form with ambiguity 6 An ambigram is a visual pun of a special kind a calligraphic design having two or more clear interpretations as written words One can voluntarily jump back and forth between the rival readings usually by shifting one s physical point of view moving the design in some way but sometimes by simply altering one s perceptual bias towards a design clicking an internal mental switch so to speak Sometimes the readings will say identical things sometimes they will say different things 2 Douglas Hofstadter Hofstadter attributed the origin of the word ambigram to conversations among a small group of friends during 1983 1984 4 Prior to Hofstadter s terminology other names were used to refer to ambigrams Among them the expressions vertical palindromes by Dmitri Borgmann 7 1965 and Georges Perec 8 9 designatures 1979 10 inversions 1980 by Scott Kim 11 12 or simply upside down words by John Langdon and Robert Petrick 12 Ambigram was added to the Oxford English Dictionary in March 2011 13 and to the Merriam Webster dictionary in September 2020 14 15 Scrabble included the word in its database in November 2022 16 17 18 History Edit Sator square word square and palindrome with the letters S and N reversed Rotational ambigram Puzzle The end by Peter Newell designed in 1893 Mirror ambigram NIPSON ANOMHMATA MH MONAN OPSIN Wash your sins not only your face in Ancient Greek in the church Hagia Sophia Turkey 19 Ambigrams published in The Strand Magazine June 1908 Many ambigrams can be described as graphic palindromes The first Sator square palindrome was found in the ruins of Pompeii meaning it was created before the Eruption of Mount Vesuvius in 79 AD A sator square using the mirror writing for the representation of the letters S and N was carved in a stone wall in Oppede France between the Roman Empire and the Middle Ages 20 thus producing a work made up of 25 letters and 8 different characters 3 naturally symmetrical A T O 3 others decipherable from left to right R P E and 2 others from right to left S N This engraving is therefore readable in four directions 21 Although the term is recent the existence of mirror ambigrams has been attested since at least the first millennium They are generally palindromes stylized to be visually symmetrical In ancient Greek the phrase NIPSON ANOMHMATA MH MONAN OPSIN wash the sins not only the face is a palindrome found in several locations including the site of the church Hagia Sophia in Turkey 19 22 It is sometimes turned into a mirror ambigram when written in capital letters with the removal of spaces and the stylization of the letter N N A boustrophedon is a type of bi directional text mostly seen in ancient manuscripts and other inscriptions Every other line of writing is flipped or reversed with reversed letters Rather than going left to right as in modern European languages or right to left as in Arabic and Hebrew alternate lines in boustrophedon must be read in opposite directions Also the individual characters are reversed or mirrored This two way writing system reveals that modern ambigrams can have quite ancient origins with an intuitive component in some minds Mirror writing in Islamic calligraphy flourished during the early modern period but its origins may stretch as far back as pre Islamic mirror image rock inscriptions in the Hejaz 23 The earliest known non natural rotational ambigram dates to 1893 by artist Peter Newell 24 Although better known for his children s books and illustrations for Mark Twain and Lewis Carroll he published two books of reversible illustrations in which the picture turns into a different image entirely when flipped upside down The last page in his book Topsys amp Turvys contains the phrase The end which when inverted reads Puzzle In Topsys amp Turvys Number 2 1902 Newell ended with a variation on the ambigram in which The end changes into Puzzle 2 In March 1904 the Dutch American comic artist Gustave Verbeek used ambigrams in three consecutive strips of The UpsideDowns of old man Muffaroo and little lady Lovekins 25 His comics were ambiguous images made in such a way that one could read the six panel comic flip the book and keep reading From June to September 1908 the British monthly The Strand Magazine published a series of ambigrams by different people in its Curiosities column 26 Of particular interest is the fact that all four of the people submitting ambigrams believed them to be a rare property of particular words Mitchell T Lavin whose chump was published in June wrote I think it is in the only word in the English language which has this peculiarity while Clarence Williams wrote about his Bet ambigram Possibly B is the only letter of the alphabet that will produce such an interesting anomaly 26 27 Characteristics EditNatural ambigrams Edit The distress signal SOS is a natural rotating ambigram OHIO a quarter turn natural ambigram The number 619 constitutes a natural ambigram but not the word western In the Latin alphabet many letters are symmetrical glyphs Most obviously the letter O The capital letters B C D E H I K O and X have a horizontal symmetry axis This means that all words that can be written using only these letters are natural lake reflection ambigrams For example BOOK CHOICE or DECIDE The lowercase letters l o s x and z are rotationally symmetrical while pairs such as b q d p m w n u and in some typefaces h y and a e are rotations of each other Thus the words sos pod suns yeah swims dollop or passed form natural rotational ambigrams More generally a natural ambigram is a word that possesses one or more symmetries when written in its natural state requiring no typographic styling The words bud bid or mom form natural mirror ambigrams when reflected over a vertical axis as does ليبيا the name of the country Libya in Arabic The words HIM TOY TOOTH or MAXIMUM in all capitals form natural mirror ambigrams when their letters are stacked vertically and reflected over a vertical axis The uppercase word OHIO can flip a quarter to produce a 90 rotational ambigram when written in serif style with large feet above and below the I Like all strobogrammatic numbers 69 is a natural rotational ambigram Patterns in nature are visible regularities of form found in the natural world 28 Similarly patterns in ambigrams are regularities found in graphemes As a consequence to this natural property some shapes appear more or less appropriate to handle for the designer Ambigram candidates can become almost natural when all the letters except maybe one or two are symmetrically cooperative for example the word awesome possesses 5 compatible letters the central s that flips around itself and the couples a e and w m Single words or several words Edit A symmetrical ambigram can be called homogram contraction of homo ambigram when it remains unchanged after reflection and heterogram when it transforms 29 30 In the most common type of ambigram the two interpretations arise when the image is rotated 180 degrees with respect to each other in other words a second reading is obtained from the first by simply rotating the sheet Single word ambigrams Edit Douglas Hofstadter coined the word homogram to define an ambigram with identical letters 29 30 In this case the first half of the word turns into the last half 12 Ambigram Wikipedia drawn by French artist Jean Claude Pertuze 180 rotational symmetry Candy 180 symmetrical ambigram Cloud vertical axis mirror ambigram with a cloud occupying negative space in the letter O Doug hypocorism for Douglas Hofstadter the father of the ambigram concept Several words Edit Three words ambigram a changing combination India Nepal associated with the invariant conjunction and A symmetrical ambigram is called heterogram 29 30 contraction of hetero ambigram when it gives another word Visually a heterogram ambigram is symmetrical only when both versions of the pairing are shown together The aesthetical appearance is more difficult to design when a changing ambigram aims to be revealed in one way only alternatively or separately because symmetry generally enhances elegance Technically there are twice more combinations of letters involved in a hetero ambigram than in a homo ambigram For example the 180 rotational ambigram yeah contains only two pairs of letters y h and e a whereas the heterogram yeah good contains four y d e o a o and h g A single word ambigram cannot be hetero but a multiple words ambigram can be homo type if the letters overlapse like in upsidedown written attached for example The ambigram saying upsidedown one way and upsidedown again the other way means it is a two words homogram But the ambigram saying upside one way and down after rotation means it is a two words heterogram There is no limitation to the number of words potentially associable and full ambigram sentences have even been published 8 12 Ambigram Wikipedia hetero type 31 True flag self referential flag horizontal axis mirror hetero type Two words ambigram Stay Here Two words ambigram Real Fake showing alternatively one version of the pair Types EditAmbigrams are exercises in graphic design that play with optical illusions symmetry and visual perception Some ambigrams feature a relationship between their form and their content Ambigrams usually fall into one of several categories 180 rotational ambigrams Edit 180 rotational ambigram saying Upside Down 32 Half turn ambigrams or point reflection ambigrams commonly called upside down words are 180 rotational symmetrical calligraphies 3 We can read them right side up or upside down or both Rotation ambigrams are the most common type of ambigrams for good reason When a word is turned upside down the top halves of the letters turn into the bottom halves And because our eyes pay attention primarily to the top halves of letters when we read that means that you can essentially chop off the top half of a word turn it upside down and glue it to itself to make an ambigram 12 Scott Kim Rotating ambigram Say Yes half turn type with 8 occurrences of the same pattern Point reflection ambigram merci Home Away 180 rotational hetero ambigram Lift half turn ambigram logo Mirror ambigrams Edit A mirror ambigram or reflection ambigram is a design that can be read when reflected in a mirror vertically horizontally or at 45 degrees 12 giving either the same word or another word or phrase Vertical axis reflection ambigrams Edit Vertical axis reflection ambigram Love you with the letter I added over like in a totem ambigram Perfect vertical axis mirror ambigram Nothing written self referential visual wordplay vertical axis reflection Historical Maoam logo candy vertical axis mirror ambigram between 1900 and 1931 When the reflecting surface is vertical like a mirror for example the calligraphic design is a vertical axis mirror ambigram The museum ambigram is almost natural with mirror symmetry because the first two letters are easily exchanged with the last two and the lowercase letter e can be transformed into s by a fairly obvious typographical acrobatics 33 Vertical axis mirror ambigrams find clever applications in mirror writing or specular writing that is formed by writing in the direction that is the reverse of the natural way for a given language such that the result is the mirror image of normal writing it appears normal when it is reflected in a mirror For example the word ambulance could be read frontward and backward in a vertical axis reflective ambigram Following this idea the French artist Patrice Hamel created a mirror ambigram saying entree entrance in French one way and sortie exit the other way displayed in the giant glass facade of the Gare du Nord in Paris so that the travelers coming in read entrance and those leaving read way out 34 Horizontal axis reflection ambigrams Edit Motel on the facade of a building is mirroring in the water of a pond to give Water self referential concept using a lake reflection Horizontal axis mirror ambigram Body Yoga When the reflecting surface is horizontal like a mirroring lake for example the calligraphic design is a horizontal axis mirror ambigram The book Ambigrams Revealed features several creations of this type like the word Failure mirroring in the water of a pond to give Success or Love changing into Lust 12 Figure ground ambigrams Edit Figure ground ambigram Michel Onfray revealing the surname in the negative space formed by the letters of the given name Figure ground ambigram Wow Mom and incidentally also a tessellation and a 180 rotational ambigram In a figure ground ambigram letters fit together so the negative space around and between one word spells another word 12 In Gestalt psychology figure ground perception is known as identifying a figure from the background For example black words on a printed paper are seen as the figure and the white sheet as the background In ambigrams the typographic space of the background is used as negative space to form new letters and new words For example inside a capital H one can easily insert a lowercase i The oil painting You amp Me US by John Langdon 1996 belongs to this category The word me fills the space between the letters of you 35 Ambigram tessellations Edit Ambigram tessellation Future 180 rotational symmetry Upside down the light color letters future occupy the negative space between the dark color letters Two tints blue and black separate each block With Escher like tessellations associated to word patterns ambigrams can be oriented in three four and up to six directions via rotational symmetries of 120 90 and 60 respectively 36 such as those created by French artist Alain Nicolas 37 Some words can also transform in the negative space but the multiplication of constraints often has the effect of reducing either the readability or the complexity of the designed words Ambigram tessellations are sorts of word puzzles in which geometry set the rules 37 Tessellation build with the natural ambigram Yeah 3 directional ambigram Serie series in French tessellation using a 120 rotational symmetry Created from a hexagon Ambigram tessellation Fuck 90 rotational symmetry Created from an isosceles right triangle Chain ambigrams Edit Chain ambigram Michel Onfray This chain ambigram nouvel an new year in French reads upside down A chain ambigram is a design where a word or sometimes words are interlinked forming a repeating chain 12 Letters are usually overlapped a word will start partway through another word Sometimes chain ambigrams are presented in the form of a circle For example the chain sunsunsunsun can flip upside down but not the word sun alone written horizontally A chain ambigram can be constituted of one to several elements A single element ambigram chain is like a snake eating its own tail A two elements ambigram chain is like a snake eating the neighbor s tail with the neighbor eating the first snake s and so on Scott Kim s Infinity works and that of John Langdon Chain reaction are also self referential since the first is infinite in the literal sense of the word and the second both reversible at 180 and interfering around the letter O evokes a chain reaction 12 Spinonyms Edit A spinonym de is a type of ambigram in which a word is written using the same glyph repeated in different orientations 12 WEB is an example of a word that can easily be made into a spinonym MBE it Motor Bike Expo spinonym logo The same glyph is repeated in three different orientations Spinonym neun 9 German for nine five times the same glyph repeated in different orientations Happy new year spinonym the same glyph in different orientations shapes the twelve letters of the sentence Perceptual shift ambigrams Edit Perceptual shift ambigram Wave and Particle by Douglas Hofstadter Ambiguous letter that can be interpreted as a H or as an A Perceptual shift ambigrams also called oscillation ambigrams are designs with no symmetry but can be read as two different words depending on how the curves of the letters are interpreted 12 These ambigrams work on the principle of rabbit duck style ambiguous images For example Douglas Hofstadter expresses the dual nature of light as revealed by physics with his perceptual shift ambigram Wave Particle 90 rotational ambigrams Edit Ignore Wrong also Wrong Ignore 90 rotational symmetry 90 rotational ambigram Jude Muslim Jew Muslim in German and incidentally also a chain ambigram Quarter turn ambigrams or 90 rotational ambigrams turn clockwise or counterclockwise to express different meanings 2 For example the letter U can turn into a C and reciprocally or the letters M or W into an E 12 Totem ambigrams Edit This historical Maria monogram is close to a totem ambigram almost symmetrical over the vertical axis The Alabama A amp M University has a totem mirror ambigram logo Words crossing or totem ambigram Hot dog vertical axis reflection symmetry A totem ambigram is an ambigram whose letters are stacked like a totem most often offering a vertical axis mirror symmetry This type helps when several letters fit together but hardly the whole word For example in the Maria monogram hu the letters M A and I are individually symmetrical and the pairing R A is almost naturally mirroring When adequately stacked the 5 letters produce a nice totem ambigram whereas the whole name Maria would not offer the same cooperativeness The ambigrammist artist John Langdon designed several totemic assemblages such as the word METRO composed of the symmetrical letter M then section ETR and below O or the sentence THANK YOU vertical assembly of T H A then of the symmetric NK couple then finally Y O U 38 Fractal ambigrams Edit In mathematics a fractal is a geometrical shape that exhibits invariance under scaling A piece of the whole if enlarged has the same geometrical features as the entire object itself A fractal ambigram is a sort of space filling ambigrams where the tiled word branches from itself and then shrinks in a self similar manner forming a fractal 39 In general only a few letters are constrainted in a fractal ambigram The other letters don t need to look like any other and thus can be shaped freely 3 Dimensional ambigrams Edit The 3D ambigram GEB for Godel Escher Bach on the cover of Hofstadter s book Three dimensional ambigram ABC A 3D ambigram is a design where an object is presented that will appear to read several letters or words when viewed from different angles Such designs can be generated using constructive solid geometry a technique used in solid modeling and then physically constructed with the rapid prototyping method 3 dimensional ambigram sculptures can also be achieved in plastic arts They are volume ambigrams The original 1979 edition of Hofstadter s Godel Escher Bach featured two 3 D ambigrams on the cover 40 Complex ambigrams Edit Complex ambigrams are ambigrams involving more than one symmetry or satisfying the criteria for several types For example a complex ambigram can be both rotational and mirror with a 4 fold dihedral symmetry Or a spinonym that reads upside down is also a complex ambigram The logo Oxo has a 4 fold dihedral symmetry mirror and 180 rotational ambigram The famous DJ Etienne de Crecy has a complex ambigram logo EDC mirroring through a horizontal axis and figure ground type with a power plug pictogram inserted in the negative space 4 fold dihedral symmetrical ambigram mirror and rotational Dig hole Die Symbols EditOther languages Edit Mirror ambigram depicting the phrase علي ولي الله Ali is the vicegerent of God in Arabic Ottoman panel between 1720 and 1730 Ambigram 곰 문 Bear Door in Korean 180 rotational symmetry The word ব ল Bangla or Bengali in Bengali half turn ambigram Ambigrams exist in many languages With the Latin alphabet they generally mix lowercase and uppercase letters But words can also be symmetrical in other alphabets like Arabic Bengali Cyrillic Greek and even in Chinese characters and Japanese kanji In Korean 곰 bear and 문 door 공 ball and 운 luck or 물 water and 롬 ROM form a natural rotational ambigram Some syllables like 응 yes 표 ticket signage or 를 object particle and words like 허리피라우 straighten your back also make full ambigrams The han character meaning hundred is written 百 that makes a natural 90 rotational ambigram when the glyph makes a quarter turn counterclockwise one sees 100 41 Media related to Ambigrams by language at Wikimedia Commons Numbers Edit Mirror and rotational ambigram of an arithmetic operation illustrating the commutative property in addition 32 Although not totally symmetrical the Sochi 2014 Olympic games official logo offers mirror and rotational symmetries linking the numbers to the letters like an ambigram Rio 2016 Olympic games half turn rotational ambigram logo containing letters and digits An ambigram of numbers or numeral ambigram contains numerical digits like 1 2 3 12 In mathematics a palindromic number also known as a numeral palindrome is a number that remains the same when its digits are reversed through a vertical axis but not necessarily visually The palindromic numbers containing only 1 8 and 0 constitute natural numeric ambigrams visually symmetrical through a mirror Also because the glyph 2 is graphically the mirror image of 5 it means numbers like 205 or 85128 are natural numeral mirror ambigrams Though not palindromic in the mathematical sense they read frontward and backward like real ambigrams A strobogrammatic number is a number whose numeral is rotationally symmetric so that it appears the same when rotated 180 degrees The numeral looks the same right side up and upside down e g 69 96 1001 42 43 44 Some dates are natural numeral ambigrams 45 In March 1961 artist Norman Mingo created an upside down cover for Mad magazine featuring an ambigram of the current year The title says No matter how you look at it it s gonna be a Mad year 1961 the first upside down year since 1881 46 Tuesday 22 February 2022 was a palindrome and ambigram date called Twosday because it contained reversible 2 two 47 48 49 Ambigrams of numbers receive most attention in the realm of recreational mathematics 2 50 Ambigrams with numbers sometimes combine letters and numerical digits Because the number 5 is approximately shaped like the letter S the number 6 like a lowercase b the number 9 like the letter g it is possible to play on these similarities to design ambigrams A good example is the Sochi 2014 Olympic games logo where the four glyphs contained in 2014 are exact symmetries of the four letters S o i and h individually 51 Other symbols Edit Palindrome with musical notes here the centre part of Alban Berg s opera Lulu As alphabet letters are glyphs used in the writing systems to express the languages visually other symbols are also used in the world to code other fields like the prosigns in the Morse code or the musical notes in music Similarly to the ambigrams of letters the ambigrams with other symbols are generally visually symmetrical either point reflective or reflective through an axis The international Morse code distress signal SOS is a natural ambigram constituted of dots and dashes It flips upside down or through a mirror In morse code the letter P coded and the letter R coded are individually symmetrical like many other letters and numbers Also the letter G coded is the exact reverse of the letter W coded Thus the combination coding the pairing G W constitutes a natural ambigram Consequently meaningful natural ambigrams written in morse code certainly exist like for example the words wog Dou or mom 3 52 53 In music the interlude from Alban Berg s opera Lulu is a palindrome thus the score made up of musical notes is almost symmetrical through a vertical axis 54 In biology researchers study the ambigrammatic property of narnaviruses by using visual representations of the symmetrical sequences 28 1 55 Fields EditArt Edit Calligraphy and typography Edit Ambigram Love Song published in a typography book Typism Calligraphic color reversal ambigram Soul of Laos published in the book Ambigrams Revealed 12 Calligraphic design Danke thanks in German and half turn ambigram Instead of simply writing them ambigram lettering covers the art of drawing letters In ambigram calligraphy each letter acts as an illustration each letter is created with attention to detail and has a unique role within a composition Lettering ambigrams do not translate into combinations of alphabet letters that can be used like a typeface since they are created with a specific candidate in mind The calligrapher graffiti writer and graphic designer Niels Shoe Meulman created several rotational ambigrams like the number fifty 12 the names Shoe Patta 12 and the opposition Love Fear 56 The cover of the 7th volume of the typography book Typism is an ambigram drawn by Nikita Prokhorov 57 The American type designer Mark Simonson designed poetic and humorous ambigrams such as the words Revelation Typophile and the symbiosis Drink Drunk 12 The last one makes a visual pun when printed on a shot glass sold commercially 58 Logos Edit The rotational logo New Man created by Raymond Loewy in 1968 is a natural ambigram The online two sided marketplace for residential cleaning Handy has a 180 rotational ambigram logo Sun Microsystems logo designed by Vaughan Pratt in 1982 chain ambigram spinonym 90 and 180 rotational symmetries Nissin Foods ambigram visual identity half turn Since they are visually striking and sometimes surprising ambigram words find large application in corporate logos and wordmarks setting the visual identity of many organizations trademarks and brands 59 In 1968 60 or 1969 Raymond Loewy designed the rotational New Man fr ambigram logo 61 62 63 The mirror ambigram DeLorean Motor Company logo designed by Phil Gibbon was first used in 1975 64 65 66 Robert Petrick designed the invertible Angel logo 12 in 1976 The logo Sun Microsystems designed by professor Vaughan Pratt 67 in 1982 fulfills the criteria of several types chain ambigram spinonym 90 and 180 rotational symmetries The Swedish pop group ABBA owns a mirror ambigram logo stylized AᗺBA with a reversed B designed by Rune Soderqvist sv 68 in 1976 69 The Ventura logo of the Visitors amp Convention Bureau s board in California cost US 25 000 and was created in 2014 by the DuPuis group It uses a 180 rotational symmetry 70 71 Other famous ambigram logos include the insurance company Aviva 72 the acronym CRD Capital Regional District in the Canadian province of British Columbia 73 the American multinational corporation DXC Technology the two sided marketplace for residential cleaning Handy 74 75 the brand name of French premium high speed train services InOui 76 the French company specializing in ticketing and passenger information systems IXXI the century old brand Maoam of the confectionery manufacturer Haribo 77 the American industrial rock band NIͶ the Japanese food company Nissin the biotechnology company Noxxon Pharma founded in 1997 the online travel agency Opodo in 2001 78 the brand of food products OXO 79 born in 1899 the video game Pod the American developer and manufacturer of audio products Sonos 80 the American professional basketball team Phoenix Suns 81 82 the German manufacturer of adhesive products UHU the quadruple symmetrical logo UA from the American clothing brand Under Armour the Canadian corporation mandated to operate intercity passenger rail service VIA in 1978 83 the American international broadcaster VOA born in 1942 and the Malaysian mobile virtual network operator XOX The student edition of the Tesco Clubcard used 180 rotational symmetry 84 Visual communication Edit Ambigram Biden USA Harris by Douglas Hofstadter conveying a political message during the 2020 United States presidential election The movie Anna by Luc Besson 2019 reveals on its poster a mirror ambigram with a vertical axis Because they are visual puns 2 ambigrams generally attract attention and thus can be used in visual communication to broadcast a marketing or political message In France a mirror ambigram Penelope benevole legible through a horizontal axis became a meme on the web after its diffusion on Wikimedia Commons 85 Penelope Fillon wife of French politician and former Prime Minister of France Francois Fillon is suspected of having received wages for a fictitious job Ironically her name through the mirror becomes benevole voluntary in French suggesting dedication for a free service Shared tens of thousands of times on the social networks this humorous ambigram made the buzz via several French 86 Belgian 87 88 and Swiss 85 medias Ambigrams are regularly used by communication agencies such as Publicis to engage the reader or the consumer through two way messages 89 Thus in 2021 male first names transformed into female first names are included in a Swiss advertising campaign aimed at raising awareness about gender equality An intriguing catchphrase typography upside down invites the reader to rotate the magazine in which the first names Michael or Peter are transformed into Nathalie or Alice 90 91 In 2015 iSmart s logo on one of its travel chargers went viral because the brand s name turned out to be a natural ambigram that read Jews upside down The company noted that we learned a powerful lesson of what not to do when creating a logo 92 Cinema posters sometimes seduce observers with ambigram titles such as that of Tenet by Christopher Nolan by central symmetry 21 or Anna by Luc Besson around a vertical axis 93 94 Ambigram meme Penelope benevole with a political message Half turn traffic sign using a directional arrow symbol to display alternatively Station Toilets Visual pun Avoid the plane to attract attention towards the environmental impact of aviation A practical application of mirror ambigrams in a banner reading Idaplatz fest front and back Zurich 2008 Comics Edit Ambigrams in comics by Gustave Verbeek in 1904 Ambigrams in comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo by Gustave Verbeek containing ambigram sentences in 1904 Another frame The American artist and writer Peter Newell published a rotational ambigram in 1893 saying Puzzle The end in the book containing reversible illustrations Topsys amp Turvys 24 In March 1904 the Dutch American comic artist Gustave Verbeek used ambigrams in three consecutive strips of The UpsideDowns of old man Muffaroo and little lady Lovekins 25 His comics were ambiguous images made in such a way that one could read the six panel comic flip the book and keep reading In The Wonderful Cure of the Waterfall 13 March 1904 an Indian medicine man says Big waters would make her very sound while when flipped the medicine man turns into an Indian woman who says punos dery eay apew poom serlem big Which is explained as poor deary several foreign words that meant that she would call the Serlem Big The next comic called At the House of the Writing Pig 20 March 1904 where two ambigram word balloons are featured The first features an angry pig trying to make the main protagonist leave by showing a sign that says big boy go away dis am home of mr h hog up side down it reads Boy yew go away We sip Home of hog pig The protagonist asks the pig if it wants a big bun upon which it replies Why big buns Am mad u which flips into In pew we sang big hym Finally in The Bad Snake and the Good Wizard 1904 Mar 27 there are two more ambigrams The first turns How do you do into the name of a wizard called Opnohop Moy the second features a squirrel telling the protagonist Yes further on only to inform it that there are No serpents here on his way back In a 2012 Swedish remake of the book 95 the artist Marcus Ivarsson redraws The Bad Snake and the Good Wizard in his own style He removes the squirrel but keeps the other ambigram How do you do is replaced by Nejnej Swedish for no and the wizard is now called Laulau Media related to Ambigrams by Gustave Verbeek at Wikimedia Commons Oubapo workshop of potential comic book art is a comics movement which believes in the use of formal constraints to push the boundaries of the medium Etienne Lecroart cartoonist is a founder and key member of Oubapo association and has composed cartoons that could be read either horizontally vertically or in diagonal and vice versa sometimes including appropriate ambigrams 96 Drawings and paintings Edit Ambigram OHO published by Rex Whistler in 1946 Ambigram OHO with reversible faces by Rex Whistler created before 1944 A young woman transforms into a grandmother Ambigram painting Me We horizontal axis mirror type 2007 The British painter designer and illustrator Rex Whistler published in 1946 a rotational ambigram OHO for the cover of a book gathering reversible drawings 97 The artist John Langdon specialist of ambigrams 59 designed many color paintings featuring ambigrams of all kinds figure ground rotational mirror or totem Among other influences he particularly admires M C Escher s drawings 12 The Canadian artist Kelly Klages painted several acrylics on canvas with ambigram words and sentences referring to famous writers novels written by William Shakespeare or Agatha Christie such as Third Girl The Tempest After the Funeral The Hollow Reformation Sherlock Holmes and Elephants Can Remember 98 Sculptures Edit Ambigram OUI NON Yes No in French by sculptor Markus Raetz installed at the top of a pole on the Place du Rhone in Geneva Switzerland observed from two angles Mia Florentine Weiss Love Hate sculpture in Munich Germany in 2020 Now Won installation in front of the Reichstag building Berlin Germany 2017 The German conceptual artist Mia Florentine Weiss built a sculptural ambigram Love Hate de 99 that has traveled Europe as a symbol of peace and change of perspective 100 Depending on which side the viewer looks at it the sculpture says Love or Hate A similar concept was installed in front of the Reichstag building in Berlin with the words Now Won Both sculptures are mirror type ambigrams symmetrical around a vertical axis 101 The Swiss sculptor Markus Raetz made several three dimensional ambigram works featuring words generally with related meanings such as YES NO 2003 102 ME WE 2004 2010 103 OUI NON 2000 2002 in French 104 105 SI NO 1996 106 and TODO NADA 1998 in Spanish 107 108 These are anamorphic works which change in appearance depending on the angle of view of the observer The OUI NON ambigram is installed on the Place du Rhone in Geneva Switzerland at the top of a metal pole Physically the letters have the appearance of iron twists With the perspective this work demonstrates that reality can be ambiguous 105 Some ambigram sculptures by the French conjurer Francis Tabary fr are reversible by a half turn rotation and can therefore be exhibited on a support in two different ways 109 110 Literature Edit Palindromes Edit Famous palindrome sentence Dogma I am God turned into a mirror ambigram The capital D at the left was changed into a lowercase d and the typographic spaces adjusted Georges Perec s vertical palindrome rotational ambigram in French Ambigrams are sorts of visual palindromes 111 Some words turn upside down others are symmetrical through a mirror Natural ambigram palindromes exist like the words wow malayalam 112 Dravidian language or the biotechnology company Noxxon that possesses a palindromic name associated to a rotational ambigram logo But some words are natural ambigrams though not palindromes in the literary acception like bud for example because b and d are different letters As a result some words and sentences are good candidates for ambigrammists but not for palindromists and reciprocally since the constraint slightly differ Authors of ambigrams also benefit from a certain flexibility by playing on the typeface and graphical adjustments to influence the reading of their visual palindromes Oulipo workshop of potential literature seeks to create works using constrained writing techniques Georges Perec French novelist and member of the Oulipo group designed a rotational ambigram that he called vertical palindrome 8 Sibylline the sentence Andin Basnoda a une epouse qui pue in French means Andin Basnoda has a smelly wife Perec did not care about punctuation spaces but his creation flips easily with a classical font like Arial Visual palindromes sometimes perfectly illustrate literary contents The American author Dan Brown incorporated John Langdon s designs into the plot of his bestseller Angels amp Demons and his fictional character Robert Langdon s surname was a homage to the ambigram artist 113 The fantasy novel Abarat written and illustrated by Clive Barker features an ambigram of the title on its cover 114 Calligrams Edit Calligram Good ambigrams representing a face and mirror self referential ambigram Reflective calligram hat in Alevism forming a human face with Arabic letters Oslo Climbing Club official logo 115 OK no acronym for Oslo Klatreklubb 90 rotational ambigram showing a human silhouette vertically A calligram is text arranged in such a way that it forms a thematically related image It can be a poem a phrase a portion of scripture or a single word The visual arrangement can rely on certain use of the typeface calligraphy or handwriting The image created by the words illustrates the text by expressing visually what it says or something closely associated In Islamic calligraphy symmetrical calligrams appear in ancient and modern periods forming mirror ambigrams in Arabic language 23 The word OK turned 90 counterclockwise evokes a human icon with the letter O forming the head and the letter K the arms and the legs The Norwegian Climbing Club Oslo Klatreklubb no acronym OK borrowed the concept of this natural calligram for their official logo 115 Semantics Edit Bilingual mirror ambigram playing on the translation of the word Lapin rabbit in French Self referential composition here away displayed in a spiral to express distance thus enhancing the meaning As described by Douglas Hofstadter ambigrams are visual puns having two or more clear interpretations as written words 2 Multilingual ambigrams can be read one way in a language and another way in a different language or alphabet 12 Multi lingual ambigrams can occur in all of the various types of ambigrams with multi lingual perceptual shift ambigrams being particularly striking Like certain anagrams with providential meanings such as Listen Silent or The eyes They see ambigrams also sometimes take on a timely sense for example up becomes the abbreviation dn very naturally by rotation of 180 116 But on the other hand it happens that the luck of the letters makes things bad This is the case with the weird anagram Santa Satan as it is with a rotational ambigram that has gone viral because of the paradoxical and unintentional message it expresses Spotted in 2015 on a metal medal marketed without bad intention the text hope displays upside down with a fairly obvious reading Adolf first name of the Nazi leader situated at the antipodes of optimism This coincidence photographed by an Internet user was relayed by several media and constitutes an ambiguous image 117 118 Mathematics Edit Ambigram of a reversible arithmetic operation Recreational mathematics is carried out for entertainment rather than as a strictly research and application based professional activity 50 An ambigram magic square exists with the sums of the numbers in each row each column and both main diagonals the same right side up and upside down 180 rotational design Numeral ambigrams also associate with alphabet letters A dissection ambigram of squaring the circle was achieved in a puzzle where each piece of the word circle fits inside a perfect square 2 Burkard Polster professor of mathematics in Melbourne 119 conducted researches on ambigrams and published several books dealing with the topic including Eye Twisters Ambigrams amp Other Visual Puzzles to Amaze and Entertain 120 In the abstract Mathemagical Ambigrams Polster performs several ambigrams closely related to his realm like the words algebra geometry math maths or mathematics 2 Message written with the digits 07734 upside down Calculator spelling is an unintended characteristic of the seven segments display traditionally used by calculators in which when read upside down the digits resemble letters of the Latin alphabet Also palindromic numbers and strobogrammatic numbers sometimes attract attention of mathematician ambigrammists 43 42 Ambigram tessellations and 3D ambigrams are two types particularly fun for the mathematician in geometry Word patterns in tessellations can start from 35 different fundamental polygons such as the rhombus the isosceles right triangle or the parallelogram 36 Word puzzles are used as a source of entertainment but can additionally serve an educational purpose The American puzzle designer Scott Kim published several ambigrams in Scientific American in Martin Gardner s Mathematical Games column among them long sentences like Martin Gardner s celebration of mind turning into Physics patterns and prestidigitation 12 Philosophy and cognition Edit Duality and analogy Edit Yin and yang symbol concept of dualism Two in one half turn ambigram In the word ambigram the root ambi means both and is a popular prefix in a world of dualities such as day night left right birth death good evil 12 In Wordplay The Philosophy Art and Science of Ambigrams 59 John Langdon mentions the yin and yang symbol as one of his major influences to create upside down words Ambigrams are mentioned in Metamagical Themas an eclectic collection of articles that Douglas Hofstadter wrote for the popular science magazine Scientific American during the early 1980s 6 Seeking the balance point of analogies is an aesthetic exercise closely related to the aesthetically pleasing activity of doing ambigrams where shapes must be concocted that are poised exactly at the midpoint between two interpretations But seeking the balance point is far more than just aesthetic play it probes the very core of how people perceive abstractions and it does so without their even knowing it It is a crucial aspect of Copycat research 6 Douglas Hofstadter Cognition and psychology Edit Ambiguity 180 rotational ambigram Legibility is an important aspect in successful ambigrams It concerns the ease with which a reader decodes symbols If the message is lost or difficult to perceive an ambigram does not work 5 Readability is related to perception or how our brain interprets the forms we see through our eyes 121 Symmetry in ambigrams generally improves the visual appearance of the calligraphic words 12 Hermann Rorschach inventor of the Rorschach Test notices that asymmetric figures are rejected by many subjects Symmetry supplies part of the necessary artistic composition 122 For many amateurs designing ambigrams represents a recreational activity where serendipity can play a fertile role when the author makes an unplanned fortunate discovery 2 26 Magic Edit Real world Prank Fake ambigram expressing illusion Ambigram Magic Dream with a handheld pattern giving a reversed shadow incredible Magical ambigram 123 In magic ambigrams work like visual illusions revealing an unexpected new message from a particular written word 124 In the first series of the British show Trick or Treat the show s host and creator Derren Brown uses cards with rotational ambigrams 125 126 These cards can read either Trick or Treat Ambiguous images of which ambigrams are a part cause ambiguity in different ways For example by rotational symmetry as in the Illusion of The Cook by Giuseppe Arcimboldo 1570 127 sometimes by a figure ground ambivalence as in Rubin vase by perceptual shift as in the rabbit duck illusion or through pareidolias or again by the representation of impossible objects such as Necker cube or Penrose triangle For all these types of images certain ambigrams exist and can be combined with visuals of the same type John Langdon designed a figure ground ambigram optical illusion with the two words optical and illusion one forming the figure and the other the background Optical is easier to see initially but illusion emerges with longer observation 128 Tattooing Edit Mirror ambigram tattoos on wrists Love Eros Handmade ambigram in tattoo New York Rich Man right side up and upside down 180 rotational ambigram tattoo No religion Ambigram tattoo Texas Sexy 180 rotational symmetry One of the most dynamic sectors that harbors ambigrams is tattooing Because they possess two ways of reading ambigram tattoos inked on the skin benefit from a mind blowing effect On the arm sleeve tattoos flip upside down on the back or jointly on two wrists they are more striking with a mirror symmetry A large range of scripts and fonts is available Experienced ambigram artists can create an optical illusion with a complex visual design 129 In 2015 an ambigram tattoo went viral following an advertising campaign developed by the Publicis group two years earlier The Samaritans of Singapore organization active in suicide prevention has a 180 reversible SOS ambigram logo acronym of its name and homonym of the famous SOS distress signal In 2013 this center orders advertisements that could be inserted in magazines to make readers aware of the problem of depression among young people and the communication agency notices the symmetrical aspect of the logo As a result it begins to produce several ambigrammatic visuals staged in photographic contexts where sentences such as I m fine I feel fantastic or Life is great turn into Save me I m falling apart and I hate myself Readers noticing this logo placed at the upper left corner of the page with an upside down typographical catchphrase rotate the newspaper and visualize the double calligraphed messages which call out with the SOS 89 130 These ads are so influential that Bekah Miles an American student herself coming out of a severe depression chooses to use the I m fine Save me ambigram to get a tattoo on her thigh Posted on Facebook the two sided photography immediately appeals to many young people impressed or sensitive to this difficulty 131 132 To educate its students George Fox University in the United States then relays the optical illusion in its official journal through a video totaling more than three million views 133 and the information is also reproduced in several local media and international organizations thus helping to popularize this famous two way tattoo 134 135 Less fortunate another teenage girl aged 16 committed suicide with her also this ambigram found on a note in her room I m fine Save me reversible calligraphy today printed on badges and bracelets for educational purposes 136 Manufacturing Edit Clothing and fashion Edit Ambigram Bounce printed inside an Adidas pink shoe Adidas marketed a line of sneakers called Bounce with an ambigram typography printed inside the shoe Several clothing brands such as Helly Hansen HH Under Armour UA or New Man fr raise an ambigram logo as their visual identity 63 Mirror ambigrams are also sometimes placed on T shirts towels and hats while socks are more adapted to rotational ambigrams The conceptual artist Mia Florentine Weiss marketed T shirts and other products with her mirror ambigram Love Hate de 137 100 Likewise the city of Ventura in California sells sweatshirts caps jackets and other fashion accessories printed with its rotational ambigram logo 138 Rotational and reflective ambigram Ideal printed on a T shirt Zen Yes embroidered on a blue T shirt with a meditation symmetrical pictogram Helly Hansen Norwegian manufacturer and retailer of clothing and sports equipment has an ambigram logo Accessories Edit Cognac Danger front and back on a set of two shot glasses Humorous warning related to alcohol consumption The CD cover of the thirteenth studio album Funeral by American rapper Lil Wayne features a 180 rotational ambigram reading Funeral Lil Wayne 139 The special edition paper sleeve CD with DVD of the solo album Chaos and Creation in the Backyard by Paul McCartney features an ambigram of the singer s name 140 The Grateful Dead have used ambigrams several times including on their albums Aoxomoxoa and American Beauty citation needed Although the words spelled by most ambigrams are relatively short in length one DVD cover for The Princess Bride movie creates a rotational ambigram out of two words Princess Bride whether viewed right side up or upside down 141 The cover of the studio album Create Destroy Create by rock band Goodnight Sunrise is an ambigram composition constituted of two invariant words create and destroy designed by Polish artist Daniel Dostal 142 The reversible shot glass containing a changing message Drink Drunk created by the typographer Mark Simonson was manufactured and sold in the market 58 The concept of reversible sign that some merchants use through their windows to indicate that the store is sometimes open sometimes closed was inaugurated at the beginning of the 2000s by a rotational ambigram Open Closed developed by David Holst 33 Creating ambigrams Edit Ambigram and tessellation Escher handmade design Different ambigram artists sometimes called ambigrammists 6 12 may create distinctive ambigrams from the same words differing in both style and form Handmade designs Edit There are no universal guidelines for creating ambigrams and different ways of approaching problems coexist A number of books suggest methods for creation including WordPlay 59 Eye Twisters 120 and Ambigrams Revealed 12 in English Ambigram generators Edit Computerized methods to automatically create ambigrams have been developed Most of them function on the simplified principle of mapping a single letter to another single letter Because of this weakness most of them can only map a word to itself or to another word that is the same length and do not combine letters Thus the generated ambigrams are in general of poor quality when compared to hand made ambigrams More sophisticated techniques employ databases of thousands of curves to create complex ambigrams citation needed Some ambigram generators are free while some others require payment Artists Edit John Langdon and Scott Kim each believed that they had invented ambigrams in the 1970s 143 Douglas Hofstadter Edit Douglas Hofstadter s mirror ambigrams featuring the names of the seven rainbow colors followed by his signature Doug Douglas Hofstadter coined the term 2 To explain visually the numerous types of possible ambigrams Hofstadter created many pieces with different constraints and symmetries 144 Hofstadter has had several exhibitions of his artwork in various university galleries citation needed According to Scott Kim Hofstadter once created a series of 50 ambigrams on the name of all the states in the US 12 In 1987 a book of 200 of his ambigrams together with a long dialogue with his alter ego Egbert G Gebstadter on ambigrams and creativity was published in Italy 4 John Langdon Edit John Langdon is a self taught artist graphic designer and painter who started designing ambigrams in the late 1960s and early 70s Lettering specialist Langdon is a professor of typography and corporate identity at Drexel University in Philadelphia 145 John Langdon produced a mirror image logo Starship in 1972 146 or 1975 better source needed that was sold to the rock band Jefferson Starship Langdon s ambigram book Wordplay was published in 1992 It contains about 60 ambigrams Each design is accompanied by a brief essay that explores the word s definition its etymology its relationship to philosophy and science and its use in everyday life 59 Ambigrams became more popular as a result of Dan Brown incorporating John Langdon s designs into the plot of his bestseller Angels amp Demons and the DVD release of the Angels amp Demons movie contains a bonus chapter called This is an Ambigram Langdon also produced the ambigram that was used for some versions of the book s cover 143 Brown used the name Robert Langdon for the hero in his novels as an homage to John Langdon 113 147 Blacksmith Records the music management company and record label possesses a rotational ambigram logo 148 designed by John Langdon 149 Scott Kim Edit Scott Kim is one of the best known masters of the art of ambigrams 62 He is an American puzzle designer and artist who published in 1981 a book called Inversions with ambigrams of many types 11 147 Other artists Edit Nikita Prokhorov is a graphic artist typographer and professional ambigrammist His book Ambigrams Revealed showcases ambigram designs of all types from all around the world 12 150 Born in 1946 Alain Nicolas is a specialist of figurative and ambigram tessellations In his book he performed many tilings with various words like infinity Einstein or inversion legible in many orientations 36 According to The Guardian Nicolas has been called the world s finest artist of Escher style tilings 151 References Edit a b Jordana Cepelewicz 2020 02 12 New Clues About Ambigram Viruses With Strange Reversible Genes Quanta Magazine Archived from the original on 2021 11 17 Retrieved 17 November 2021 a b c d e f g h i j k Polster Burkard Mathemagical Ambigrams PDF Retrieved 2020 03 29 a b c Witherellspecial Jim 2022 02 27 In a word Wow the many ways words are symmetrical Sun Journal Maine Archived from the original on 2022 05 04 Retrieved 2022 12 06 a b c Douglas R Hofstadter Indiana University 2007 03 21 Retrieved 2021 08 07 a b Deciphering the art of ambigrams Adobe Retrieved 2021 08 08 a b c d Hofstadter Douglas 2008 Metamagical Themas Questing For The Essence Of Mind And Pattern Basic Books p 880 ISBN 978 0786723867 Borgmann Dmitri 1965 Language on Vacation An Olio of Orthographical Oddities Scribner p 27 ASIN B0007FH4IE a b c L ecrit touareg du sable au papier Un typographe francais a retranscrit l alphabet des hommes du desert Liberation in French 1996 07 27 Retrieved 2021 08 10 Ce repere Perec PDF APMEP Association des Professeurs de Mathematiques de l Enseignement Public in French Retrieved 2021 08 07 OMNI magazine September 1979 page 143 work of Scott Kim a b Kim Scott 1986 1981 Inversions A Catalog of Calligraphic Cartwheels Byte Books ISBN 978 0070345461 a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab Prokhorov Nikita 2013 Ambigrams Revealed A Graphic Designer s Guide To Creating Typographic Art Using Optical Illusions Symmetry and Visual Perception New Riders ISBN 978 0133086461 Latest update March 2011 List of new words Oxford English Dictionary Archived from the original on 2011 04 10 Retrieved 2021 08 28 Definition of ambigram Merriam Webster Archived from the original on 2020 09 15 Retrieved 2021 09 20 Words We re Watching Ambigram Merriam Webster Archived from the original on 2021 09 23 Retrieved 2021 09 20 Scottie Andrew 2022 11 16 Scrabble adds 500 new playable words like vax deepfake and Jedi CNN Atlanta Archived from the original on 2022 11 20 Retrieved 2022 12 06 Mouriquand David 2022 11 18 Scrabble adds 500 new words to its official dictionary Euronews Lyon Archived from the original on 2022 11 24 Retrieved 2022 12 06 Words Added to the Scrabble Dictionary Merriam Webster Springfield Massachusetts 2022 11 16 Archived from the original on 2022 12 05 Retrieved 2022 12 06 a b R Langford James A Dictionary of the Eastern Orthodox Church Ayer 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The Doodle Bug The Telegraph Archived from the original on 2022 01 12 Retrieved 6 November 2016 Hofstadter Douglas R 1986 Les Ambigrammes Ambiguite Perception et Balance Esthetique in French Castella pp 157 187 Wordsmith John Langdon and the art of the ambigram Citypaper Archived from the original on 2008 07 24 Retrieved 2021 08 07 Langdon John Starship johnlangdon net John Langdon Retrieved 6 November 2016 a b Wow Mom It s an Ambigram The New York Times 2011 04 07 Archived from the original on 2020 12 22 Retrieved 2021 08 07 Blacksmith home page blacksmithnyc Retrieved 2021 08 07 Blacksmith John Langdon John Langdon Archived from the original on 2022 01 21 Retrieved 2021 08 16 Center Stage Nikita Prokhorov Logolounge Retrieved 2021 08 07 Can you solve it The Guardian 11 February 2019 Retrieved 2021 08 07 Further reading EditHofstadter Douglas R Metafont Metamathematics and Metaphysics Comments on Donald Knuth s Article The Concept of a Meta Font Scientific American August 1982 republished with a postscript as chapter 13 in the book Metamagical Themas ISBN 9780553346831 Hofstadter Douglas R Ambigrammi Un microcosmo ideale per lo studio della creativita Ambigrams An Ideal Microworld for the Study of Creativity Hopefulmonster Editore Firenze 1987 in Italian ISBN 9788877570062 Langdon John Wordplay Ambigrams and Reflections on the Art of Ambigrams Harcourt Brace 1992 republished 2005 ISBN 9780151984541 Polster Burkard Eye Twisters Ambigrams amp Other Visual Puzzles to Amaze and Entertain Constable 2008 ISBN 9781402757983External links EditAmbigram at Wikipedia s sister projects Definitions from Wiktionary Media from Commons Data from Wikidata Ambigrams at Curlie Retrieved from https en wikipedia org w index php title Ambigram amp oldid 1141665132, wikipedia, wiki, book, books, library,

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