Hats off to the artists—it takes real talent and dedication to make a good tessellation.
|John A. L.||Osborn||USA|
Dr. David Annal (1934-2008) was the original author and designer of Tessellations.org. An excellent diagnostic physician, he was well known for his sense of humor and ability to prod people into thinking more clearly and creatively. His three major hobbies were his tessellation art, his cats and dogs, and his membership in a computer enthusiasts' club.
His logical and inquiring mind, which made him a practical doctor, also led him to meld computers into his wide range of interests. His interest in the works of J.S. Bach led to learning about the math behind the music, which led him to the math of fractals, which led to the world of tessellations.
(The above is summarized from his computer club obituary and his bio on Tessellations.org.)
The president of Japan Tessellation Design Association.
The first exhibition of his tessellations was on his web site in 1993, very early era of world wide web. His elephant design won first prize in the first tessellation contest on the web held by World of Escher in 1994. His wild boar design was named one of the Best Things in Art Online by BYTE Magazine in 1995. His tessellation software 'Escher Paint Contest' won the first Java language contest by Sun Microsystems, Inc in 1995.
In 1998, at the Escher Congress in Rome, Yoshiaki met the legendary tessellation artist Makoto Nakamura, and they founded the Japan Tessellation Design Association. The association provides workshops, exhibitions, and publications on tessellations.
Recent workshop: T3 puzzle workshop.
Recent exhibition: Japan Tessellation Design - its progress and prospects.
Recent publication: Enjoy mathematical puzzles with M. C. Escher.
I am an artist without mathematical background, although I now consider myself a mathematician more than an artist due to my exposure to Escher.
My introduction to Escher was through browsing (in about 1983) a Reader’s Digest magazine of March 1981. This contained a brief article on Escher titled “The Artist Who Aims to Tease” by Greg Keeton, with a handful of Escher’s prints. Amongst these was Day and Night, which intrigued me, and I wondered how Escher did this highly unusual artwork. However, not understanding how to go about such matters, I put it aside. Show more...
Not until 1986 did I turn my attention to tessellations in a practical sense, when my interest in art moved from conventional landscapes to more cerebral concerns — surrealism and op art. As op art can be described as mathematical, this led me to Escher’s works in op art books and then in mathematical books. I then left “conventional” art behind in favour of tessellations, both Escher-like and purely mathematical.
Unusually, my interests cover the whole range of tessellations, namely Escher-like, mathematical, and historical. Special interests include writing on Escher, the Cairo tiling, houndstooth, and pavements, each with many entries on my website. I say “unusually”, as people interested in tessellation tend to be of a single focus and often do not venture outside their chosen domain of art or mathematics.
The only advice I would give to an aspiring designer is not to think that Escher did everything and so there’s nothing left. Or to think that it is way beyond your ability (I am a case in point). There are many animal motifs that Escher overlooked, or simply ignored (not to mention inanimate motifs). Many artists show work equal to, if not better, than Escher! It can be done. Alain Nicolas is a shining example, although there are others.
He discovered M. C. Escher in the library of Felix V. Festa Junior High School, where the card in his favorite Escher book contained his name repeatedly (without other names) for the two years he attended. Stupidly, he guessed that the grayscale etchings were pencil sketches, and so he threw himself into a 30-year period in which he used pencils in preference to all other art tools. He did not develop a strong interest in color or painting until hospitalized for several months in Hiroshima in the year 2000, when a friend gifted him with water-color pencils and a water "fude" (brush pen). Show more...
He variously made his living as a language, art, and computer skills teacher, computer advice newspaper columnist, magazine illustrator and editorial cartoonist, website designer, submarine co-pilot (yes, really), computer nerd/repairman/teacher, SCUBA instructor, and Japanese-English-German translator.
Seth was initally drawn only to M. C. Escher's trick perspective pictures, not to his tessellations. It wasn't until 2005 that he began doing tessellation. The inspiration and drive came when someone told him, “I think the lizard motif in tessellation has pretty much been used up.” The same year, Seth won his first of three consecutive first prizes in the international tessellation contest run twice yearly by “World of Escher” (dot com) from about 1995 to about 2010. The contest-winning entries were Baby Alligators and Tessellated Lions (the lizard tessellation that arose from that moment of inspiration), Bootlickers, and The Circle of Pegasus.
(The above is summarized from his bio on Tessellations.org.)
As a child of 5 in 1949 I was given a shiny, brand-new Australian penny for my tram fare home, and I fell in love with the splendid image of Australia’s national animal, our beautiful Kangaroo. It is truly Australia’s icon, and having raised adorable orphan joeys myself, my love for Kangaroos has no bounds. Yes that’s an awful pun (), but it’s true too.
Forward 20 years to 1969 — I first saw Escher’s Sky and Water tessellation, and I was astounded!
What magic was this! Lifelike ducks and fishes, perfectly concatenating in an infinitely repeatable pattern, with no waste space and no overlaps! In all history, no-one until Escher had ever created such patterns! How could that be? Show more...
From then on, I wanted to do just one design that could stand unashamed alongside those of The Master.
How hard could it be? ... H’mmmmm ... ? Where do you even start?
Later, around 1996, after doing a few tesses myself, I recorded this feeling in rhyme on my website:
Once I saw a sketch by Escher: Sky and Water is its name
It’s Ducks and Fishes actually, but precious just the same.
Those beasties blew my brainbox – I was never so impressed:
So then I tried to tessellate – Put Escher under pressure, Mate! –
Well, excel those at any rate: to better Escher’s best!
(It continues, as you may see on my site.)
It took me until 1993 to manage even one respectable tess, and then it happened not by effort but by a chance perception ...
... One day I was at a boring meeting, doodling stick-figure Kangaroos, and suddenly I saw that the space above the back and tail of a west-facing Kangaroo could neatly fit the southern coast of Australia’s map. Then I found that three more, with persuasion, could define the Eastern, Northern and Western parts of our coast.
It took a lot of re-drawing: my technique is to use a soft (2B) pencil: I’m left-handed (as was Escher) and my handwriting is horrid! I do many light spidery lines which can easily be erased without damage to the paper using BluTack (that’s a hint folks!), making successive approximations of ideal shapes. Hundreds and hundreds of lines, until I find the best I can. That was my technique then and remains so today. But in the end, to my delight, I had a very creditable translational tessellation which I called OZZIE the Magic Kangaroo, remarkably marrying Australia’s twin icons, even including our baby Island State of Tasmania. And I loved it! (See it on my site.)
I didn’t even know then that tesses were of interest to mathematicians. But then, a complete stranger named Paul Scott, Professor of Pure Maths at Adelaide Uni, rang me to enquire about it. I don’t even know how he heard about it, but anyway, the upshot was that in 1996, at his invitation, I wrote the centrefold article about it in The Australian Mathematics Teacher, a very well-thought-of educational magazine of which Paul was Editor. My experience eerily echoes Escher’s own, where he records that, having been largely ignored by the Art community in Holland, he found his way from a beautiful but lonely “garden” of his own kind of art to “the open gate of mathematics” through which he passed to acceptance, and eventually to eternal international acclaim.
And in my case, that recognition by Prof Scott, the realisation that tessellation was so much more than decoration, encouraged my interest as never before.
Kangaroos had not finished with me — they still haven’t! For the Sydney Olympics in 2000 I drew and re-drew them in many sporting poses — skiing, boxing, high- and long-jumping, playing basketball, riding a bike, archery and more! And in the process I found a handful of other Kangaroo tessellations, some of which you may see on my own site – and one, TwoRoos, was The One I had always wanted.
TwoRoos fulfilled my every personal demand: it is my favourite type of tessellation, a “glide reflection”, of my favourite animal, basically very true-to-life, in its iconic position, i.e. full but relaxed flight. That is the one on this Tiled.art site, and Thank You Very Much Rick!
By then I had become even more fascinated by figurative tessellation generally, and gradually my little menagerie grew to include Elephants (which are remarkably obliging), Koalas, Seahorses and more, including some designs which are not animals: maps of Australia itself, Plane Tree leaves (for the pun on ‘regular division of the plane’! ... though the erudite Maths Teacher and author Jill Britton, a Canadian, thought they were Maple! ); and so on.
Unfortunately for me, I am a mathematical ignoramus, and I am not at all handy with graphics programs either. My “technique” for designing tesses, if it can be termed that, comes not from grids or patterns to start with, but from perceptions of possibilities in random shapes ... markings on bark or blobs of squashed chewing gum on pavements or crumpled kitchen paper or cloud formations ... I remember Escher’s son telling of how his father would pick out suggestive animal shapes on a stuccoed wall in their bathroom and accentuate them for the rest of the family’s entertainment. I imagine that some of his tesses found their origin in that way. So my painful quest for any given design starts at total chaos, and progresses to absolute order – I guess a shrink would be able to draw some conclusions about my mind but anyway that’s how it is. If I find a feature that keys with something that looks interesting – e.g., a Kangaroo’s head with another’s front paws and belly – I torture the animals to try to make them fit all around, which mostly physical laws of nature insist that they only do with extreme difficulty, if at all.
But when they do, it’s marvellous.
And then and only then is when a regular pattern emerges, and at last I perceive the underlying grid.
I don’t wish to do endless numbers of tesses: I try to make my victim creatures as lifelike and proportionate as possible, which severely limits my subjects: it tends to preclude cartoonish graphics for me. I avoid straight lines, as computer graphics often involve; I don’t do fantastic creatures like winged dragons, while big hair and flowing clothing to fill space are not acceptable. And there are now so many tesses of birds, fishes and dogs that I am not interested in adding more, though I’ve done a few of each myself. Australia has provided me with many unique creatures which few others have attempted: Platypus, Koala, Leafy Sea-Dragons, Numbats, Cockatoos, so many others! I always try to show all 4 limbs of quadrupeds, plus other prominent features such as big ears and tails. That’s not easy: many tesses of horses or dogs have only 3 or 2 legs visible, which I find a bit unsatisfying. With Kangaroos, as you may see, I was lucky: for one thing, Escher didn’t try to tessellate any (he would’ve probably found TwoRoos if he had!) and for another, Yes, Kangaroos are quadrupeds but their legs operate in unison, in pairs, so in profile they look like they are two-legged, plus tail. As in that beautiful Penny image.
One cannot invent tessellations, if you see what I mean: the design you bring to light has always been there waiting to be discovered. But once discovered and defined it is eternal!
What is it about tessellations anyway?
Whence this strange power to fascinate mathematicians and artists alike, and even those not usually interested in art or maths?
Why are Escher exhibitions nowadays, fifty years after his death, always crowded with people of all ages, genders, educational levels, staring, ooh-ing and ahh-ing?
Is it because everyone everywhere would like everything to fit perfectly, in every sense?
Is it because of the implication of infinity in every tessellation, which would gladly extend beyond the stars if given an endless plane to play on?
Is it because you’re wondering ... ???! How in the world ...???
If I had to offer a technical psychological explanation, I would say that it’s because the duality inherent in every line animates and tickles our usually somnolent and cynical schizophrenic nerve. That nerve can’t quite believe it, and in some people, it itches like mad. I know because I’m one of them. At 79 I’m still fascinated, and still attempting the odd tessellation, right now one of mummy ’Roos with joeys, one of pretty fan-dancers!
— Bruce Bilney
P.S. I do indeed love tessellations, but my first love is rhyming verse because only language conveys thought. Much of my verse is eco-educational – those animals I’ve tessellated are always close to my thoughts, and I’ve managed to combine my facility with verse with my much-lower-proficiency with drawing, as you may see on my site. Most of my graphics on that site have a verse to keep them company.
Confidentially, I think that what might have been the section of my brain that should have been learning about Mathematics (and money) spent so much time with lines running around in my head, with homophones and scansion and emphasis and that sort of ilk, that it atrophied ...
Human and animal figures, perfectly nested into each other, complex and identical mosaic pieces filling the surface of prints. Tessellations pushed far beyond their traditional limits; all symmetries explored. A nontraditional field, there are only a handful of women around the globe that have tackled tessellations. Learning the craft by hand and screen printing have been replaced with tablet, and giclée prints. An explosion of artwork, fuelled by a connection to an unending flow of creativity, intuition, unusual perception, with a touch of French comic books. “If I can make you tilt your head, and smirk, I’ve done my job as a tessellation artist.”
I also teach classes on learning tessellations.
Andrew Crompton is an architect and lecturer who has been drawing tilings since 1985.
He started his website in 1997 in an effort to find everyone in the world who shared this interest, last updating it in 2009 when 54 people had come forward.
His Lifelike Tessellations paper shows abstract examples of the isohedral tessellation types which have no straight edges. But he adds a slight correction—IH15 was mistakenly included as it contains two straight edges, so there should be 48 tilings rather than 49.
As a young child I developed a love of dinosaurs, drawing, painting and visiting museums and art galleries. I joined a local art group in my early teens, exhibiting mostly landscapes and gaining regular sales and commissions.
It was during my first year of teaching in the mid 1980s that I taught some basic tessellation to children and began to experiment myself, eventually setting myself the task of tessellating a Stegosaurus. After unexpectedly succeeding I then attempted several other creatures and managed to complete a small number of finished tessellation works, After exhibiting an early Brontosaurus tessellation in an 'Artists in Essex' exhibition I was invited to exhibit some more dinosaur tessellations for a separate exhibition at the Minories, Colchester. Several years later, with a little more free time after a change of career, I developed some more designs and exhibited at the Naze tower, Walton on the Naze. Show more...
I still paint occasional landscapes but the tessellation of dinosaurs and other extinct animals has become something of an obsession. I see each creature as a puzzle to be solved and have recently worked out rough designs for another 40 or so (—enough to keep me busy for quite a while!)
Being something of a dinosaur myself I continue to work with traditional materials, developing and refining shapes using pencil and tracing paper, then producing finished paintings in oil or watercolour. Unfortunately it's a VERY laborious process! I have also become increasingly concerned with making the animals as anatomically correct as possible, though in palaeontology all reconstructions are subject to change and unfortunately some of my older paintings are clearly based on old, outdated reconstructions. C'est la vie...
I have recently finished building an art studio in the garden, thus providing a much needed dedicated space for creative work. Now I just need to spend the time in there!
Maurits Cornelis Escher (1898-1972) was the pioneer of tessellation art. Without ever seeing a tessellation of recognizable figures he drew 137 of his own, independently working out the structures for 28 of the 35 symmetries shown on this site.
Early on, Escher was fascinated by the intricate tile works in the Alhambra (Granada, Spain), discovering fresh symmetries like this one, which inspired one of his first drawings. But he noted that the Alhambra artists never used realistic motifs, or asymmetric tiles, both of which interested him greatly. Show more...
In 1937 he showed some early tessellations to his brother George (a geology professor), who suggested reading some crystallography papers. Setting aside the intimidating mathematics Escher immediately saw inspiring ideas in the illustrations. He became intensely focused on tessellations, completing 60 drawings by 1942 along with a thorough notebook of coherent theory he called “Regular division of the plane with asymmetric congruent polygons”. With this theory as a framework he made tessellation drawings steadily for the rest of his life. You can see 110 of them in this gallery, or follow links below to the 63 with single motifs.
Escher didn’t consider his drawings to be completed artworks, giving them only numbers and never titles. But they were a fertile source for other works — tessellations staged with other elements and beautifully rendered as lithographs and woodcuts, like his famous Day and Night and Reptiles.
Escher always wondered why nobody else was pursuing similar work. In a 1960 lecture to an overflow crowd he said “I can hardly believe that throughout the centuries no one has ever hit on the idea, that a plane-pattern might be made more significant and more fascinating by using as building components concrete, recognizable shapes borrowed from nature, such as fishes, birds, reptiles or human beings. But I do not give up hope of sometime meeting such a like-minded spirit; who knows, perhaps one of you may be able to help me! At all events, I urge you to please let me know if you should ever encounter such a plane-pattern, made up of recognizable elements.” (Schattschneider p.42)
Since then his brilliant “plane-patterns” themselves have inspired artists worldwide to create like-minded art, as well as captivating millions of viewers. ... Show less
(The above is summarized from Doris Schattschneider’s fine book M.C. Escher: Visions of Symmetry.)
Tatsuo Horiuchi posts tessellations regularly to Instagram and Pinterest, and weekly to his blog.
I am a freelance illustrator living in New Jersey. Most of my work consists of creature and character design, storyboards and animatics, logo design, and illustration for books, advertising, and table top role-playing games. My numerous explorations into tessellations have, so far, just been personal side projects.
All of my current tessellations were created using Tessella, an outdated add-on that can only be used on long outdated versions of Adobe Illustrator. I use Photoshop to paint in details and textures onto the tiles created in Illustrator. The whole process, using various means to even get the outdated software to partially function is extremely clunky and prone to crashes, so it's a small victory to be able show a finished piece.
Jos Leys (1952-?) is a retired mechanical engineer who has always had a keen interest in anything mathematical. As an admirer of M.C. Escher he tried to produce tesselations himself using the Ultrafractal software. His other interests are 3D fractals, and producing mathematical images and animations using the PovRay software. Jos lives in Belgium.
The tessellations I draw are all figurative tessellations. The first time I encountered tessellation was in M.C. Escher's Horsemen around 1970. The reason I stick to figurative tessellation is that I still remember the excitement and shock I felt at that time.
I felt that the lives trapped in these crystals were the very memory of the history of the universe, from the beginning of the universe to all life. This universe is seamlessly connected, from chaos to patterns, to life. The exhilarating feeling of running through it all at once is the real thrill of creating a figurative tessellation.
tessellation art is a language for expressing the world, and the goal of my work is to use the words of tessellation to depict the “story of life.” For that reason, I have made various attempts so far to see what kind of expressions are possible with tessellation. I will continue to do so as long as possible.
And now, what I’m working on the most is an experiential tessellation art that can be played in a puzzle format by tessellating as many kinds of animals as possible. Panic Zoo is scheduled to be exhibited in its entirety at the Hamada World Children’s Museum from March 2023.
私が描くテセレーションは、すべて具象テセレーションです。 私が初めてテセレーションに出会ったのは、1970年頃でM.C.エッシャーの版画 騎士でした。 私が具象テセレーションにこだわる理由は、その時の興奮と衝撃を今でも覚えているからです。
アートにおけるテセレーションそのものは、世界を表現するための一つの言語に過ぎず、私の作品の目的は、テセレーションという言葉を使って、"生命の物語 "を描き出すことです。 そのために、テセレーションでどのような表現が可能なのか、これまで様々な試みを行ってきました。それは今後も可能な限り続けていくつもりです。
I was born in Paris on February 10, 1946. I did no artistic or mathematical studies, and I worked many different jobs.
As a child, I loved to draw. But the various attempts left me dissatisfied. Realistic drawing seemed to me without interest – there was the photo. And then, as Pascal said: “What vanity is painting which attracts admiration by the resemblance of things whose originals we do not admire.” Drawing differently, there were a thousand ways. But everything I saw either made me laugh or left me indifferent or appalled. Show more...
Alas, I forgot the drawing...
And a lot of time passed...
Around my 30s, my eyes fell on a curious, unusual, unique, magical drawing... yes, magical. I spent more time that day contemplating this drawing than I had previously spent looking at others. It was the work of a man named Escher. I immediately started looking for the various achievements of this “unknown”. Perhaps he had done something else that was worthy of interest!
I soon found myself at the door of a marvelous, fantastic garden. A garden whose construction was a hymn to intelligence. A garden full of humor in the contours and illusions in the detours. A garden where the smallest touch was in harmony with nature and mathematics. A garden where each motif expressed humility and respect in the face of infinity. A garden whose structures were eternal. It was the “garden of the division of the plane into figurative motifs.”
And a miracle happened...
I had once again become “the child who likes to draw”.
But family and work left me little time. It wasn't until I retired that I really got into it. In 2005, “Éditions Belin Pour la Science” published my book “Parcelles d'infini”. In 2015, that being exhausted, I posted it on my site http://tessellations-nicolas.com.
This is how I see my art:
Unlike pictorial art in general where too often you may do anything, figurative tiling keeps you in the realm of the universal natural order. No other graphic art has these constraints that force you to stay close to nature.
Every line you draw goes in this direction, and you have to do it and redo it until reaching perfection. You are not in control. You share your own requirements with those of the laws of the universe. You do not create. You are only a revealer. And because of its specificity in being infinitely reproducible, the figurative tiling offers the most beautiful approach through the imagination, of the absolute and of eternity. ... Show less
Je suis né à Paris le 10 février 1946. Je n'ai fait aucune étude artistique ou mathématique, et j’ai fait beaucoup de métiers.
Enfant, j'aimais dessiner. Mais les différentes tentatives me laissaient insatisfait. Dessiner réaliste me semblait sans intérêt, il y avait la photo. Et puis, comme le disait Pascal : «Quelle vanité que la peinture qui attire l’admiration par la ressemblance des choses dont on admire point les originaux ». Dessiner autrement, il y avait mille façons. Mais tout ce que je voyais, soit me faisait rire, soit me laissait indifférent ou consterné. Montre plus...
Las, j'oubliais le dessin…
Et beaucoup de temps passa…
Vers mes 30 ans, mon regard se posa sur un dessin curieux, inhabituel, unique, magique… oui, magique. Je passais plus de temps ce jour-là à contempler ce dessin que je n'en avais passé jusqu’alors à en regarder d’autres. C’était l’œuvre d’un dénommé Escher. Je me mis aussitôt en quête des différentes réalisations de cet «inconnu». Peut-être avait-il fait autre chose qui fut digne d’intérêt !
Beauté divine !
Je me trouvai bientôt à la porte d’un jardin merveilleux, fantastique. Un jardin dont la construction était un hymne à l’intelligence. Un jardin plein d’humour dans les contours et d’illusions dans les détours. Un jardin où la plus petite touche était en harmonie avec la nature et les mathématiques. Un jardin où chaque motif exprimait l’humilité et le respect devant l’infini. Un jardin dont les structures étaient éternelles. C’était le «jardin de la division du plan en motifs figuratifs».
Et un miracle se produisit…
J’était redevenu «l’enfant qui aime dessiner».
Mais la famille et le travail ne me laissaient que peu de temps. Ce n'est qu'à ma retraite que je m'y suis vraiment investi. En 2005, les éditions «Pour la Science» ont édité mon livre "Parcelles d'infini". En 2015, celui-ci étant épuisé, je l'ai reporté sur mon site http://tessellations-nicolas.com/
Voilà comment je vois mon art :
Au contraire de l’art pictural en général où trop souvent l’on fait n’importe quoi, le pavage figuratif vous maintient dans le domaine de l’ordre naturel universel. Aucun art graphique ne possède ces contraintes qui vous oblige à rester proche de la nature.
Chaque trait que vous tracez va dans ce sens et vous devez le faire et le refaire jusqu’à la perfection. Vous n’en êtes pas maître. Vous partagez vos propres exigences avec celles des lois de l’univers. Vous ne créez pas. Vous n’êtes qu’un révélateur. Et de par sa spécificité à être reproduisible à l’infini, le pavé figuratif offre la plus belle approche par l’imagination, de l’absolu et de l’éternité. ... Montrer moins
Hidekazu Nomura posted 61 fine tessellations on Instagram over four months in 2019, using 20 different tessellation symmetries.
Any contact information would be greatly appreciated — please send an email to [email protected].
John A. L. Osborn (1929-2017) coined the term amphography for the process of creating a figurative tile — “drawing, with each side of one's line, a different part of the same figure” (from the Greek amph, “both”, and graph, “to draw”). He writes that this “double-duty” outline differs radically from the ordinary sort of outline that merely divides figure from ground. With amphography there is no ground — only the same figure in multiple interlocking copies.
He worked with pencil and paper only (not a computer), focusing on a particular subject. Sometimes he was surprised when the final geometry wasn’t the one he started with, as when “an initial quadrilateral basis became hexagonal in the finished tiling”. He studied ceramics and made actual tiles for some of his artworks, like Little Miss Muffet.
In addition to his gallery of tessellation art he worked extensively on variable tilings. He created two tile sets that can be assembled in infinitely many ways — one with 10 bat and lizard figures and one with 8 beetle figures — with many example tilings.
See also his biography and obituary.
I was born in Paris in 1966, and studied mathematics at Pierre and Marie Curie University (Paris 6).
In the 2000s, I made figurative tessellations in the style of Escher and designed a classification algorithm according to the work of mathematician Xavier Hubaut which made it possible to unify Fedorov's algebraic and Heesch's topological classifications.
Subsequently, I embarked on figurative sculpture by applying in 3D the principles of the tiling of the plane. I was invited to retrospectives on Escher in Italy (Mostra de Bologna Milan, Florence…) which earned me a quote on the M. C. Escher Wikipedia page (Italian) in the Fortuna critica section.
Je suis né à Paris en 1966, j’ai étudié les mathématiques à l’université P et M Curie Paris 6.
Dans les années 2000, j’ai réalisé des pavages figuratifs dans le style d’Escher et conçu un algorithme de classification selon les travaux du mathématicien Xavier Hubaut qui ont permis d’unifier les classifications algébrique de Fedorov et topologique de Heesch.
Je me suis aussi interessé aux pavages du plan en réseaux de cercles concentriques et de spirales logarithmiques et des surfaces 3D.
Par la suite, je me suis lancé dans la sculpture figurative en appliquant en 3D les principes des pavages du plan. J’ai été invité aux rétrospectives sur Escher en Italie (Mostra de Bologne Milan, Florence…) ce qui m’a valu une citation sur la page Wikipedia de M. C. Escher (italienne) dans la partie Fortuna critica.
My educational background is in Neuroscience, but I've always been drawn to creative and artistic pursuits. I love making things and solving puzzles. Tessellation design is both!
I've recently been trying to work my designs into more minimalist formats that feature only a few tiles and obscure the underlying repetition. My hope is that this will make the discovery of the symmetries feel fresh and exciting to viewers, rather than being their first impression of my work. I'd like for my designs to be recognizable and aesthetic even outside of the tessellated context. You can see these designs, and purchase prints or products featuring them, at my Etsy shop called “TiledWild”. Show more...
My approach to tessellation doesn't begin with the symmetry type or underlying tile shape. Many tutorials online will tell you to begin with a triangle, or a square, then cut and shift pieces around to produce your tessellating tile. I find this an incredibly difficult design process that doesn't easily reveal opportunities for good compromise.
The central challenge in tessellation design is that each component must play two different roles. A good design is a compromise between the needs of each role such that the final product can be easily interpreted in both ways. So I begin my designs by sketching different possible outlines for my shape, and looking for pieces that can be matched together. Areas of high and low detail, sharp and soft curves, etc. can be paired. I experiment with intermediate shapes that might fit both roles when viewed from different angles. Only then do the limitations of the larger symmetry pattern come into play, as certain parts of the tile will be forced together depending on the ways that others are paired.
I've created an experimental tessellation design program based on this approach which I call Tessella. You can play with it on my website. The basic concept is to draw a single segment at a time, which is automatically repeated across a set of reference locations to form a tessellating design. I've provided a tool that allows for nudging parts of these segments around to tweak the design. I would love to hear feedback or see designs that come from this tool! Feel free to contact me on my Instagram or YouTube accounts. ... Show less
They are done digitally and I have sold a couple as large printouts on a canvas roll. They were secured to a wall like a large patterned quilt.
The above is summarized from an imagekind post. Any contact information would be greatly appreciated — please send an email to [email protected].
DB Sullivan is an artist, poet, and web designer. His website (archived) shows 15 tessellations, as well as detailed drawings with reflection, refraction, and perspective, and nursery rhymes for grown-ups.
(The above is summarized from his website.)
The “garden” that Escher pointed to is beautiful and fertile, and many people now visit it. I am one, and the tessellations presented here could be seen as a record of my playing in that garden.
When I create a tessellation I impose only one condition — that each tile must stand alone as a “picture”. The word “picture” here does not mean the level of realism, rather that it is expressed without excess or deficiency in relation to the objective. Therefore, the beauty of the borders (silhouettes) and the diversity of symmetry may be sacrificed. I understand this and consider it my challenge for the future.
I hope you can find your own idea of ”beauty” in this garden...
I am an illustrator and designer from Düsseldorf, Germany. In 1966 I was born in Switzerland and my talent for drawing was given to me as a gift in my cradle, so studying illustration in Strasbourg (France) and Offenbach (Germany) was an obvious choice.
My enthusiasm for M. C. Escher was sparked in my youth on forays through my parents’ bookshelves. At that time I came across an illustrated book by the exceptional artist whose “impossible figures”, optical illusions, and mysterious metamorphoses fascinated me deeply. Inspired by Escher’s work, I began to develop my own tessellations thirty years ago.
It is important to me that viewers can recognize my figures by simple outline rather than relying on surface details. This demand has enabled me over the years to market some tessellations industrially, and so my passion also became a business. Over time I started to combine my tessellations with a story, and illustratively present them as a picture.
On my specially created Instagram account I regularly post my latest works, and I look forward to your visit!
Sakuramederu is my pen name ("I love cherry blossoms"). I was born in 1960 in Tokyo, Japan, and studied economics at university.
I'm an amateur artist, since I've never earned money from tessellation art until now. I use paper and pencil, and go back and forth to Photoshop.
My first policy is to make figures that are recognizable by shape, without adding detail inside the tiles.
My second policy is to start with a realistic figure and modify the outline so it tessellates, rather than starting with a plain polygon and deforming it to find a figure.
Please see these explanations of how I work.