Ambigram

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Ambigram of the word ambigram. 180deg rotational symmetry Ambigram of the word ambigram - rotation animation.gif
Ambigram of the word ambigram. 180° rotational symmetry

An ambigram is a calligraphic design that has several interpretations as written. [1]

Contents

Etymology

The word ambigram was coined by Douglas Hofstadter, an American scholar of cognitive science, best known as the Pulitzer Prize winning author of the book Gödel, Escher, Bach.

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. [1]

Hofstadter describes an ambigram as a "calligraphic design that manages to squeeze two different readings into the selfsame set of curves."[ citation needed ]

Different ambigram artists (sometimes called ambigramists) may create distinctive ambigrams from the same words, differing in both style and form.[ citation needed ]

History

Mirror ambigram NIPsONANOMEMATAMEMONANOPsIN (Wash your sins, not only your face) inscribed in ancient Greek upon a holy water font outside the site of the church Hagia Sophia. All the letters are symmetrical vertically, with the N stylized [?] in the right part, so the sentence can be read the same way in two directions. Ambigram palindrome NIPsONANOMEMATAMEMONANOPsIN (Wash your sins, not only your face, in Greek).jpg
Mirror ambigram ΝΙΨΟΝΑΝΟΜΗΜΑΤΑΜΗΜΟΝΑΝΟΨΙΝ (Wash your sins, not only your face) inscribed in ancient Greek upon a holy water font outside the site of the church Hagia Sophia. All the letters are symmetrical vertically, with the N stylized Ͷ in the right part, so the sentence can be read the same way in two directions.
Rotational ambigram Puzzle / the end by Peter Newell, 1893 Ambigram - puzzle - the end - by Peter Newell 1893 - book Topsys and turvys (crop).jpg
Rotational ambigram Puzzle / the end by Peter Newell, 1893
Ambigrams by Gustave Verbeek (1904) - comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo - At the house of the writing pig.jpg
Comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo - At the house of the writing pig by Gustave Verbeek containing ambigram sentences (March 1904).
Ambigrams Chump, honey, M. H. Hill, Bet, and five more words - Strand Magazine 1908.jpg
Early ambigrams published in The Strand Magazine , June 1908

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 [3] found in several locations, including the site of the church Hagia Sophia, [2] in Istanbul, Turkey. 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 (Ͷ).

The first sator square palindrome was found in the ruins of Pompeii, that means it was created before 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 [4]

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. It was a common way of writing in stone in Ancient Greece.

Ottoman mirror ambigram panel depicting the phrase `ly wly llh (Ali is the vicegerent of God, in Arabic), between 1720 and 1730 Mirror writing2.jpg
Ottoman mirror ambigram panel depicting the phrase علي ولي الله ( Ali is the vicegerent of God, in Arabic), between 1720 and 1730

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.

The earliest known non-natural rotational ambigram dates to 1893 by artist Peter Newell. 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. [5] His comics were ambiguous images, made in such a way that one could read the 6 panel comic, flip the book and keep reading. In The Wonderful Cure of the Waterfall [6] (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'. [7] 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.[ clarification needed ] 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.'. [8] 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'. [9] Finally in The Bad Snake and the Good Wizard [10] (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. [11] These ambigrams are all relatively simple compared to contemporary designs, but given the constraints that Verbeek had due to the drawing and story they are impressive nevertheless.[ who said this? ] In a 2012 Swedish remake of the book, [12] 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 no) and the wizard is now called 'Laulau'.

From June to September 1908, the British monthly The Strand published a series of ambigrams by different people in its "Curiosities" column. [13] 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." [13]

Rotational faces as optical illusion are very old, since metal coins with reversible figures were produced in 1550, and maybe earlier. In this perspective, a 180° rotational ambigram "¡OHO!" was published in 1946 for the cover of a book gathering reversible drawings by Rex Whistler.

Popularity

Rotational ambigram logo New Man created by Raymond Loewy in 1969 Ambigram New Man logo metal button on a shirt animated gif.gif
Rotational ambigram logo New Man created by Raymond Loewy in 1969

In 1969, Raymond Loewy designed the rotational New Man  [ fr ] ambigram logo, [14] [15] which is still in use in 2020. [16] The mirror ambigram DeLorean Motor Company logo was first used in 1975. [17] [18]

John Langdon and Scott Kim also each believed that they had invented ambigrams in the 1970s. [19] Langdon and Kim are probably the two artists who have been most responsible for the popularization of ambigrams.[ original research? ] John Langdon produced the first mirror image logo[ verification needed ] "Starship" in 1975. [20] [ better source needed ] Robert Petrick, who designed the invertible Angel logo in 1976, [21] was also an early influence on ambigrams.[ according to whom? ]

The earliest known published reference to the term ambigram was by Hofstadter, who attributed the origin of the word to conversations among a small group of friends during 1983–1984.[ citation needed ] The original 1979 edition of Hofstadter's Gödel, Escher, Bach featured two 3-D ambigrams on the cover.

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. [19] Brown used the name Robert Langdon for the hero in his novels as an homage to John Langdon. [22]

In music, the Grateful Dead have used ambigrams several times, including on their albums Aoxomoxoa and American Beauty .

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

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. [23]

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.” [24]

Types

ambigram << Upside Down >> Ambigram Upside Down.png
ambigram « Upside Down »
Animated ambigram "Biden USA Harris" with rotational symmetry of 180 degrees, created and drawn by Douglas Hofstadter for the 2020 United States presidential election. Biden-USA-Harris ambigram animated.gif
Animated ambigram “Biden USA Harris” with rotational symmetry of 180 degrees, created and drawn by Douglas Hofstadter for the 2020 United States presidential election.

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:

3-Dimensional
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.[ citation needed ]
Chain
A design where a word (or sometimes words) are interlinked, forming a repeating chain. Letters are usually overlapped meaning that a word will start partway through another word. Sometimes chain ambigrams are presented in the form of a circle. [25]
Dihedral
A natural mirror-image ambigram consisting of numerical digits.
Figure-ground
A design in which the spaces between the letters of one word form another word. [25]
Fractal
A version of space-filling ambigrams where the tiled word branches from itself and then shrinks in a self-similar manner, forming a fractal. See Scott Kim's fractal of the word "TREE" for an animated example. [26]
Mirror-image
A design that can be read when reflected in a mirror, usually as the same word or phrase both ways. Ambigrams that form different words when viewed in the mirror are also known as glass door ambigrams, because they can be printed on a glass door to be read differently when entering or exiting. [25]
Multi-Lingual
An ambigram that can be read one way in one language and another way in a different language. Multi-lingual ambigrams can exist in all of the various styles of ambigrams, with multi-lingual perceptual shift ambigrams being particularly striking. The name sinosign has been proposed for the case of the shift being between Latin script and Chinese script.[ citation needed ]
Natural
A natural ambigram is a word that possesses one or more of the above symmetries when written in its natural state, requiring no typographic styling. For example, the words "dollop", "sos", "SᙡIᙢS", "suns" and "pod" form natural rotational ambigrams. In Korean, (bear) and (door) form a natural rotational ambigram. In some fonts, the word "seas" forms a natural rotational ambigram. The word "bud" forms a natural mirror ambigram when reflected over a vertical axis, as does "ليبيا", the name of the country Libya in Arabic. The words "BOX", "CHOICE" and "OXIDE", in all capitals, form natural mirror ambigrams when reflected over a horizontal axis. The longest such word is CHECKBOOK. The words "HIM", "TOOTH", "MAXIMUM", "TOY" and "WHOM", in all capitals, forms natural mirror ambigrams when their letters are stacked vertically and reflected over a vertical axis. See the article transformation of text for a discussion of letter symmetry.[ citation needed ]
Perceptual Shift (Oscillation)
A design with no symmetry but can be read as two different words depending on how the curves of the letters are interpreted. [25]
Rotational
A design that presents several instances of words when rotated through a fixed angle. This is usually 180 degrees, but rotational ambigrams of other angles exist, for example 90 or 45 degrees. The word spelled out from the alternative direction(s) is often the same, but may be a different word to the initially presented form. A simple example is the lower-case abbreviation for "Down", dn, which looks like the lower-case word up when rotated 180 degrees.[ citation needed ]
Strobogrammatic
A natural rotational ambigram consisting of numerical digits.
Space-Filling
Similar to chain ambigrams, but tile to fill the 2-dimensional plane.[ citation needed ]
Spinonym
An ambigram in which all the letters are made of the same glyph, possibly rotated and/or inverted. WEB is an example of a word that can easily be made into a spinonym. Previously called rotoglyphs or rotaglyphs. [27]
Symbiotogram
An ambigram that, when rotated, can be read as a different word than the original, e.g., "LIFE" would read as "DEATH". [28]

Totem

An ambigram whose letters are stacked. May be rotational or mirrored.

Creating ambigrams

Handmade designs

Handmade ambigram for a tattoo << New York / Rich Man >> Ambigram tattoo New York Rich Man.jpg
Handmade ambigram for a tattoo «  New York / Rich Man »

There are no universal guidelines for creating ambigrams, and there are different ways of approaching problems. A number of books suggest methods for creation (including WordPlay [29] and Eye Twisters [30] ).

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. Most ambigram generators are free, while some others require payment.[ citation needed ]

Other names

Ambigrams have also been called, among other things:

See also

Related Research Articles

Palindrome Word, phrase, number, or other sequence of units that may be read the same way in either direction

A palindrome is a word, number, phrase, or other sequence of characters which reads the same backward as forward, such as madam or racecar. There are also numeric palindromes, including date/time stamps using short digits 11/11/11 11:11 and long digits 02/02/2020. Sentence-length palindromes ignore capitalization, punctuation, and word boundaries.

<i>Gödel, Escher, Bach</i> 1979 book by Douglas Hofstadter

Gödel, Escher, Bach: an Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter. By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher, and composer Johann Sebastian Bach, the book expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how, through self-reference and formal rules, systems can acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.

Symmetry Mathematical invariance under transformations

Symmetry in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article.

Boustrophedon Form of writing, left-to-right and right-to-left in alternate lines

Boustrophedon is a style of writing, mostly seen in ancient manuscripts and other inscriptions, in which alternate lines of writing are flipped, or reversed, with reversed letters — rather than always flowing left-to-right as in modern European languages, or right-to-left as in Arabic and Hebrew. It was a common way of writing in stone in ancient Greece.

Crossword Word puzzle and word search game

A crossword is a word puzzle that usually takes the form of a square or a rectangular grid of white- and black-shaded squares. The game's goal is to fill the white squares with letters, forming words or phrases, by solving clues, which lead to the answers. In languages that are written left-to-right, the answer words and phrases are placed in the grid from left to right ("Across") and from top to bottom ("Down"). The shaded squares are used to separate the words or phrases.

Wallpaper group Classification of a two-dimensional repetitive pattern

A wallpaper group is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles and tiles as well as wallpaper.

Mirror writing

Mirror writing 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. It is sometimes used as an extremely primitive form of cipher. A common modern usage of mirror writing can be found on the front of ambulances, where the word "AMBULANCE" is often written in very large mirrored text, so that drivers see the word the right way around in their rear-view mirror.

Rigid body Physical object which does not deform when forces or moments are exerted on it

In physics, a rigid body is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass.

Rotational symmetry Symmetry (something looking the same) under rotation

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.

Gustave Verbeek Dutch-American illustrator and cartoonist (1867-1937)

Gustave Verbeek was a Dutch-American illustrator and cartoonist, best known for his newspaper cartoons in the early 1900s featuring an inventive use of word play and visual storytelling tricks.

Sator Square A word square containing a five-word Latin palindrome

The Sator Square is a two-dimensional word square containing a five-word Latin palindrome. It features in early Christian as well as in magical contexts. The earliest example of the square dates from the ruins of Pompeii, which some scholars attribute to pre-Christian origins, such as Jewish or Mithraic.

Ambiguous image image that exploits graphical similarities between two or more distinct images

Ambiguous images or reversible figures are visual forms which create ambiguity by exploiting graphical similarities and other properties of visual system interpretation between two or more distinct image forms. These are famous for inducing the phenomenon of multistable perception. Multistable perception is the occurrence of an image being able to provide multiple, although stable, perceptions. Classic examples of this are the rabbit-duck and the Rubin vase. Ambiguous images are important to the field of psychology because they are often research tools used in experiments. There is varying evidence on whether ambiguous images can be represented mentally, but a majority of research has theorized that they cannot be properly represented mentally. The rabbit-duck image seems to be one of the earliest of this type; first published in Fliegende Blätter, a German humor magazine ; the My Wife and My Mother-in-Law drawing, which dates from a German postcard of 1888, is another early example.

A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down. A strobogrammatic prime is a strobogrammatic number that is also a prime number, i.e., a number that is only divisible by one and itself. It is a type of ambigram, words and numbers that retain their meaning when viewed from a different perspective, such as palindromes.

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. Each digit may be mapped to one or more letters, creating a limited but functional subset of the alphabet, sometimes referred to as beghilos.

A dihedral prime or dihedral calculator prime is a prime number that still reads like itself or another prime number when read in a seven-segment display, regardless of orientation, and surface. The first few decimal dihedral primes are

John Langdon is an American graphic designer, ambigram artist, painter, and writer.

Constrained comics is a form of comics that places some fundamental constraint on form beyond those inherent to the medium. By adding a constraint, the artist is attempting to produce original art within tightly defined boundaries.

The nucleic acid notation currently in use was first formalized by the International Union of Pure and Applied Chemistry (IUPAC) in 1970. This universally accepted notation uses the Roman characters G, C, A, and T, to represent the four nucleotides commonly found in deoxyribonucleic acids (DNA). Given the rapidly expanding role for genetic sequencing, synthesis, and analysis in biology, researchers have been compelled to develop alternate notations to further support the analysis and manipulation of genetic data. These notations generally exploit size, shape, and symmetry to accomplish these objectives.

Transformations of text are strategies to perform geometric transformations on text, particularly in systems that do not natively support transformation, such as HTML, seven-segment displays and plain text.

References

  1. 1 2 Polster, Burkard. "Mathemagical Ambigrams" (PDF). Retrieved 2020-03-29.
  2. 1 2 R. Langford-James, A Dictionary of the Eastern Orthodox Church, Ayer Publishing, ISBN   0-8337-5047-X, p. 61.
  3. Barry J. Blake, Secret Language: Codes, Tricks, Spies, Thieves, and Symbols, Oxford University Press, 2010, ISBN   0-19-957928-8, p. 15.
  4. Verbeek, Gustave (2009). The Upside-Down World of Gustave Verbeek. Sunday Press. ISBN   978-0976888574.
  5. c:File:Ambigrams by Gustave Verbeek (1904) - comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo - The wonderful cure of the waterfall.jpg
  6. c:File:Ambigrams by Gustave Verbeek (1904) - comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo - The wonderful cure of the waterfall (panel 4).jpg
  7. c:File:Ambigrams by Gustave Verbeek (1904) - comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo - At the house of the writing pig (panel 4).jpg
  8. c:File:Ambigrams by Gustave Verbeek (1904) - comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo - At the house of the writing pig (panel 5).jpg
  9. c:File:Ambigrams by Gustave Verbeek (1904) - comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo - The bad snake and the good wizard.jpg
  10. c:File:Ambigrams by Gustave Verbeek (1904) - comics The Upside Downs of Little Lady Lovekins and Old Man Muffaroo - The bad snake and the good wizard (panel 5).jpg
  11. Ivarsson, Marcus (2012). Uppåner med lilla Lisen & gamle Muppen. Epix. ISBN   9789170895241.
  12. 1 2 Newnes, George (1908). "Curiosities". The Strand Magazine. No. 36. p. 359. Retrieved 6 November 2016.
  13. "Raymond Loewy Biographie". Raymond-loewy.un-jour.org (in French). Archived from the original on 8 June 2009. Retrieved 6 November 2016.
  14. Pierce, Scott (20 May 2009). "Typography Two Ways: Calligraphy With a Twist". Wired . Wired.com. Retrieved 6 November 2016.
  15. "New Man" (in French). Archived from the original on 23 October 2019. Retrieved 20 April 2020.
  16. "1975 Prototype Logo". Car and Driver . July 1977. Retrieved 6 November 2016. In 1977, only the single 1975 prototype existed. Note that there are multiple visible differences between the prototype vehicle and later production models, including the design of the front end.
  17. "Motor City eyebrows were raised when DeLorean married model Cristina Ferrare". US Magazine . 1 November 1977. Retrieved 6 November 2016.
  18. 1 2 Bearn, Emily (4 December 2005). "The Doodle Bug". The Telegraph . Retrieved 6 November 2016.
  19. Langdon, John. "Starship". johnlangdon.net. John Langdon . Retrieved 6 November 2016.
  20. "Angel Logo". angelrocks.com. 2 October 2009. Archived from the original on 7 November 2016. Retrieved 6 November 2016.
  21. Brown, Dan (21 December 2005). "As a tribute to John Langdon, I named the protagonist Robert Langdon". Popularculture.it (in Italian). Retrieved 6 November 2016.
  22. "The Princess Bride (20th Anniversary Widescreen Edition) (Bilingual)". amazon.ca. Retrieved 6 November 2016.
  23. Hoffman, Jenn (9 May 2015). "This Charger that Says 'Jews' Is Today's Tech Fail". motherboard.com. Vice . Retrieved 6 November 2016.
  24. 1 2 3 4 "Types of Ambigrams | John Langdon". John Langdon. Retrieved 2018-10-17.
  25. Kim, Scott (1981). "Tree". scottkim.com. Retrieved 6 November 2016.
  26. See Hofstadter, Ambigrammi, p. 48.
  27. Prokhorov, Nikita (2013). Ambigrams Revealed: A Graphic Designer's Guide To Creating Typographic Art Using Optical Illusions, Symmetry, and Visual Perception. New Riders. pp. 51, 124. ISBN   9780133086461.
  28. Langdon, John (2005). WordPlay. Bantam Press. ISBN   0-593-05569-1.
  29. Polster, Burkard (2007). Eye Twisters. Constable. ISBN   978-1-84529-629-2.
  30. Borgmann, Dmitri (1965). Language on Vacation: An Olio of Orthographical Oddities . Scribner. p. 27. ASIN   B0007FH4IE.
  31. OMNI magazine, September 1979, page 143, work of Scott Kim.
  32. Kim, Scott (1980). Inversions: Catalogue of Calligraphic Cartwheels . McGraw-Hill Inc., US. ISBN   0-07-034546-5.

Further reading