thumb|Animation of a half-turn ambigram of the word ambigram, with 180-degree rotational symmetry
An ambigram is a calligraphic composition of glyphs (letters, numbers, symbols or other shapes) that can yield different meanings depending on the orientation of observation.
Ambigrams can be constructed in various languages and 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 1979 book Gödel, Escher, Bach.
It is a neologism composed of the Latin prefix ambi- ("both") and the Greek suffix -gram ("drawing, writing"). "The essence is imbuing a single written form with ambiguity".
<gallery mode="packed" class="center">
File:Ambigram Say Yes radial pattern rainbow color - rotation animation.gif|Rotating ambigram "Say Yes", half-turn type with 8 occurrences of the same pattern, created by Basile Morin. The phrase itself is a phonetic palindrome.
File:Ambigramme Merci - animation.gif|Point reflection ambigram merci. By Basile Morin.
File:Ambigram Home Away - red and yellow - animation.gif|"Home / Away", 180° rotational hetero-ambigram by Basile Morin.
File:Lift London red circle logo.svg|"Lift", half-turn ambigram logo.
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Reflection
A mirror or reflection ambigram is a design that can be read when reflected in a mirror vertically, horizontally, or at 45 degrees,
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.
Horizontal axis
thumb|"[[Motel" on the facade of a building is mirroring in the water of a pond to give "Water", self-referential concept by Basile Morin using a lake reflection.]]
thumb|left|Horizontal axis mirror ambigram y Basile Morin "[[Human body|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".
Figure-ground
thumb|left|Figure-ground ambigram [[Michel Onfray, revealing the surname in the negative space formed by the letters of the given name. By Basile Morin.]]
thumb|Figure-ground ambigram "Liar / Jail" (and incidentally also a [[tessellation). By Basile Morin.]]
In a figure / ground ambigram, letters fit together so the negative space around and between one word spells another word.
Tessellations
thumb|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. By Basile Morin.]]
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, such as those created by French artist Alain Nicolas. 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 word puzzles, in which geometry sets the rules.
Spinonyms
A is a type of ambigram in which a word is written using the same glyph repeated in different orientations. WEB is an example of a word that can easily be made into a spinonym thanks to the graphic similarities among its letters.
<gallery class="center">
File:Motor Bike Expo logo.svg| (Motor Bike Expo) spinonym logo. The same glyph is repeated in three different orientations.
File:Spinonym neun.JPG|Spinonym "neun 9" (German for nine), the same glyph repeated five times in different orientations.
File:Ambigram spinonym Happy New Year.png|"Happy New Year" spinonym, by Basile Morin, features the same glyph in different orientations shaping the twelve letters of the sentence.
</gallery>
Perceptual shift
thumb|Perceptual shift ambigram, [[Wave-particle duality|Wave and Particle, by Douglas Hofstadter.]]
thumb|left|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.
Totem
thumb|left|This historical Maria [[monogram is close to a totem ambigram, almost symmetrical over the vertical axis.]]
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 , 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 ambigram 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.
Fractal
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.
In general, only a few letters are constrained in a fractal ambigram. The other letters don't need to look like any other, and thus can be shaped freely.
3-dimensional
thumb|left|The 3D ambigram "GEB" (for [[Gödel, Escher, Bach) on the cover of Hofstadter's book.]]
thumb|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.
Complex
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.
<gallery mode="packed" class="center" heights="180">
File:Oxo_Bouillon_Liebig,_Reclams_Universum_1905.jpg|The logo Oxo has a 4-fold dihedral symmetry (mirror and 180° rotational ambigram).
File:EDC logo.svg|The famous DJ Étienne de Crécy 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.
File:Ambigram Dig hole Die.png|4-fold dihedral symmetrical ambigram (mirror and rotational) "Dig hole, Die".
</gallery>
Other glyphs
Symbols
Some symbols like summation (Σ), dollar ($) and the equals sign (=) are symmetrical.
Languages
thumb|left|Mirror ambigram depicting the phrase [[wikt:علي|علي ولي الله (Ali is the vicegerent of God, in Arabic), Ottoman panel, between 1720 and 1730.]]
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".
.
Numbers
thumb|left|Mirror and rotational ambigram of an arithmetic operation illustrating the [[commutative property in addition.]]
An ambigram of numbers, or numeral ambigram, contains numerical digits, like 1, 2, 3...
Some dates are natural numeral ambigrams.
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."
Tuesday, 22 February 2022, was a palindrome and ambigram date called "Twosday" because it contained reversible 2 (two).
Ambigrams of numbers receive most attention in the realm of recreational mathematics.
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.
Other uses
thumb|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 "gnaw" , "Dou" or "mom" .
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.
In August 1976, Douglas Hofstadter premiered in Stanford a canon in the form of a fully symmetrical score, reversible 180 degrees, ornamented with three ambigrams.
In biology, researchers study the ambigrammatic property of narnaviruses by using visual representations of the symmetrical sequences.
Fields
Art
Calligraphy and typography
thumb|left|Ambigram [[Love song|Love Song published in a typography book (Typism).]]
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", the names "Shoe / Patta", and the opposition "Love / Fear".
The cover of the 7th volume of the typography book Typism is an ambigram drawn by Nikita Prokhorov.
The American type designer Mark Simonson designed poetic and humorous ambigrams, such as the words "Revelation", "Typophile", and the symbiosis "Drink / Drunk". The last one makes a visual pun when printed on a shot glass, sold commercially.
Logos
thumb|Logo of [[Voice of America.]]
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.
In 1968 or 1969, Raymond Loewy designed the rotational ambigram logo.
The mirror ambigram DeLorean Motor Company logo, designed by Phil Gibbon, was first used in 1975.
Robert Petrick designed the invertible Angel logo in 1976.
The logo Sun (Microsystems) designed by professor Vaughan Pratt 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 in 1976.
The Ventura logo of the Visitors & Convention Bureau's board, in California, cost and was created in 2014 by the DuPuis group. It uses a 180° rotational symmetry.
Other famous ambigram logos include: <!-- by alphabetical order -->
the insurance company Aviva;
the acronym CRD (Capital Regional District) in the Canadian province of British Columbia;
the American multinational corporation DXC Technology;
the two-sided marketplace for residential cleaning Handy;
the brand name of French premium high-speed train services InOui;
the French company specializing in ticketing and passenger information systems IXXI;
the century-old brand Maoam of the confectionery manufacturer Haribo;
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;
the brand of food products OXO born in 1899;
the video game Pod;
the American developer and manufacturer of audio products Sonos;
the American professional basketball team Phoenix Suns;
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;
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.
Visual communication
thumb|Ambigram "[[Joe Biden|Biden USA Harris" by Douglas Hofstadter conveying a political message during the 2020 United States presidential election.]]
thumb|The movie [[Anna (2019 feature film)|Anna by Luc Besson (2019) reveals on its poster a mirror ambigram with a vertical axis.]]
Because they are visual puns,
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, Belgian and Swiss
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".
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."
Cinema posters sometimes seduce observers with ambigram titles, such as that of Tenet by Christopher Nolan, by central symmetry.
<gallery mode="packed" class="center">
File:Penelope_benevole_ambigramme_de_Basile_Morin.jpg|Ambigram meme "Penelope / benevole" with a political message.
File:Ambigram_station_toilets_-_animated.gif|Half-turn traffic sign using a directional arrow symbol to display alternatively "Station / Toilets".
File:Ambigram_Avoid_the_plane.gif|Visual pun "Avoid the plane" to attract attention towards the environmental impact of aviation.
File:IdaplatzAmbigram.jpg|A practical application of mirror ambigrams in a banner reading "Idaplatz fest" front and back (Zürich, 2008).
</gallery>
Comics
thumb|upright|Ambigrams in [[comics by Gustave Verbeek in 1904.]]
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. 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'.
.
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.
Drawings and paintings
thumb|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.
The artist John Langdon, specialist of ambigrams,
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.
Sculptures
thumb|left|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.]]
The German conceptual artist Mia Florentine Weiss built a sculptural ambigram , that has traveled Europe as a symbol of peace and change of perspective. 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.
The Swiss sculptor Markus Raetz made several three-dimensional ambigram works, featuring words generally with related meanings, such as
YES-NO (2003),
ME-WE (2004, 2010),
OUI-NON (2000–2002) in French,
SI–NO (1996)
and TODO-NADA (1998) in Spanish
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.
Tattoos
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.
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.
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.
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 and the information is also reproduced in several local media and international organizations, thus helping to popularize this famous two-way tattoo.
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.
Literature
Palindromes
thumb|left|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.]]
thumb|[[Georges Perec's "vertical palindrome" (rotational ambigram), in French. Some words turn upside down, others are symmetrical through a mirror. Natural ambigram palindromes exist, like the words "wow", "malayalam" (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 constraints differ slightly. 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.
The fantasy novel Abarat, written and illustrated by Clive Barker, features an ambigram of the title on its cover.
Calligrams
thumb|left|[[Calligram "Good ambigrams" representing a face and mirror self-referential ambigram.]]