Many artists, teachers, and students ask whether their art can appear on If you're considering submitting tessellation art for posting on, this essay is a great starting point.

Most importantly, ask yourself whether your art *is* tessellation. The guideline I use on this site is, "Does it fit together like a jigsaw puzzle, without gaps or overlaps, to completely fill a surface?" If you're not sure your art fits the definition, read through this other essay: "Is it a Tessellation or not?"

For kids' art, I tend to accept a lot of art that DOES NOT completely fit the definition of tessellation, simply to encourage budding artists and avoid broken hearts. On the other hand, displaying art that isn't a proper tessellation only encourages imitators who may think "Ah, that's all right then." For this reason, I've decided to develop a rating system that will appear beside all future guest art. It will indicate whether the art completely or only partially fits the guidelines for a tessellation, and give some indication of where the worrying bit, if any, might be. More detail about that rating system appears further toward the end of this essay.


We don't expect every 10-year-old kid to be a fully developed Leonardo da Vinci. If a bird's head is bigger than his body, we won't reject the art. We've already accepted a half dozen "monster" tessellations featuring monsters who look like they swallowed bowling pins and lost a fight with Godzilla. We've got pictures of fish with their fins on backwards, and birds who couldn't fly if their nest was afire.

Neither do we expect all the art to be Escher style, in the sense of using a plant/animal/thing motif. Our website,, originally accepted only Escher-style tessellations. Since then, however, we have broadened our minds to accept abstract geometric tessellations, also known as "Islamic" or "Alhambra style" tessellations. To read more about the difference between Escher-style tessellations and Islamic-style tessellations, please visit our essay on "Escher or Abstract?"


Please, do your best. Work up to a reasonable level of artistic ability and cleverness. If you've only drawn a few hexagons on a napkin, don't expect us to clap enthusiastically, honor your half-hearted attempt, and show your work on Let's explore what I mean, first for Escher-style tessellations and then for Islamic-style, and lastly, explain how the same shape can be a valid Islamic-style tessellation but fail as an Escher-style tessellation.

In an Escher-style piece, your art should show that you've tweaked the outline of the tiles to make the tiles look as much like your target motif as possible. In other words, if you make a shape that tessellates and then think "Hey, it looks a little like a chicken", DO NOT STOP THERE. Use a bit of cleverness and the rubber end of the pencil to alter that outline. Improve the resemblance. Make the tessellating shape as much like a chicken shape as you can. THEN it's ready to be displayed here.

In an Islamic-style tessellation which you want to show us, it's OK to stick with the basic geometric shape, but we're looking for "wow" feelings inspired by the geometry. Show us that you've invested heaps of thought in trying different shapes and arrangements to get heaps of the "wow, that's awesome inspiring math" feeling from your audience. If you keep the tessellation abstract but start using non-basic shapes, that's even better... but again, we're going to expect the art to have some kind of consistent feeling and inspire people to say "That's clever. Wow." The opposite is: if you send us a picture of unmodified chickenwire or boring square bricks, don't expect applause.

Please understand the difference between mathemtically correct tessellation and artistically correct Escher-style tessellation. That first one is OK for an Islamic style tessellation, but it can stop being a proper tessellation if the artist fills in interior details that make the basic shapes look like they overlap or have gaps. Consider these examples:

This is an OK tessellation.
The design at left is a simple but OK Islamic style (abstract geometric) tessellation. It fills the space without gaps or overlaps, like a simple jigsaw puzzle. I strongly wish the artist had invested more time and effort to make the design clever with lots of "wow" factor, but this is... OK. It fits the definition of a tessellation: it fills the space with repeated shapes, and shows no gaps nor overlaps.
bad tessellation chevrons This is NOT a good tessellation.
The design at left is the same outline as the good tessellation above it, but now it's trying to look like houses. See the windows? Now, it's not an Abstract style tessellation. It's trying to be Escher-style, and it is NOT a tessellation. Why not? Well, the windows tell us "these are houses." Although the windows don't affect the outline of the houses, they DO give us important clues about what that outline must be. If they're houses, then their outlines should be flat along the bottom, like the bottom of a square. So.. it's obvious that these houses overlap. The pointy roofs overlap the houses above-and-behind them.
This is an OK tessellation.
It's abstract, so it's an "Abstract style" tessellation. The shapes fit together in a repetitive pattern, without gaps or overlaps. The shape is a little unusual and lopsided, but it does follow the guidelines for a tessellation.
This is NOT a good tessellation.
The tile at left has the same outline as the good Islamic tessellation above it, but now it's trying to be an Escher style tessellation. It looks like elephants and water. The water is the problem: water doesnt' have a definite shape, so it looks like a gap. The gap is a watery background showing around the elephant shapes. Also, it's lazy art because the artist has clearly made no effort to make the left side of the shape look like the back of an elephant. This is art I would (and did) put in's guest gallery because a young child tried her best, but it is not an ideal example of tessellation art.

Without entering a contentious religious debate, it's worth noting that Islamic artists often obey the letter of that law, but not its spirit: some Islamic calligraphy is, despite that ban, shaped like real things... like horses and chickens, for example.

Also, think about the awe inspired by art that just shows off the "wow" factor of geometry without being a picture of a person or animal. The alhambra's geometric art is not "real things"-- not representational art, that is. But, it's so beautiful as geometry and math interwoven, that the resulting abstract art is as awe-inspiring and attention-grabbing as the painting of Mona Lisa. It's not difficult to imagine that it could become an idol, an object of worship. The Alhambra is already a tourist attraction, and many theologians talk about the awe and balance of math as a way to feel a religious kind of awe.

So, for me, the personal decision is to allow Islamic tessellations because they can be just as beautiful, and demostrate as much brain power, as Escher-style tessellations. I've eased away from Dr. David Annal's initial strict prohibition against showing geometric/ Islamic/ Alhambra/ non-representational art. However, just like the Escher-style art I show here, I *do* insist that any of that other kind of tessellation be of a high grade, showing high artistic value and showing that an effort has been made to tweak the outlines for some artistic reason.

Gimme sizzle, not fizzle.

For example, if the whole tile seems to be a mostly organic (swoopy, curly, no-straight-lines)shape then it shouldn't show its original "corners" or walls-- observers shouldn't be able to quickly guess, or see leftovers of, the simple geometric "cell" (the geometric shape that the tessellation started as). The original tessellation shape's flat lines and sharp corners shouldn't be visible in, say, an organic, swoopy style that the artist is aiming for. Put simply, the artist should show that s/he's not being lazy, and that s/he is tweaking the tiles toward some definite artistic goal. If it looks like a meaningless, flavorless blob or just a minor tweaking of a simple geometric shape, I won't be impressed.

For an example in the other direction entirely, if a tessellation is all sharp corners and recognizable geometric shapes like stars, diamonds, and triangles then the artist had darned well better be showing me something awesome, not something that looks as been-there-done-that as brickwork or chicken wire.

brick tessellation chicken wire hexagons

So: would we post some abstract tessellations from guest artists on Sure... but they'll have to be of a high standard and in some way "move" the observer: it should inspire awe or fascination or some other emotion.

My criteria for acceptable abstract tessellations and Escher-style tessellations are a bit vague, but I hope I've given you some sort of guide so you can predict whether to send your art to us for publication on