The Two Kinds of Tessellation Art

Tessellations can be divided into two groups: those which are pictures of "real things" like people, pencils, housepets, and piranhas... fish or fishhooks or fishermen... and those which aren't. The others are more abstract and give you a "wow!" feeling from the beauty of the math ... the geometry ... that's in them.

The earliest tessellations were simple stone floors, walls, path,s and brick walls.

In Roman times, tessellations often made pictures, but the pictures were made of small colored simple square tiles. The pictures were large groups of square colored tiles which, when viewed together, looked like a big bull or battlefield or orchard, and so on. Your computer screen is a little like that. Look at it very closely, and you'll see that the picture on your computer screen is a big picture made from tiny square or rectangular things called "pixels". Those Roman tessellations were neither Escher nor Abstract style.

That first kind is often called Escher-style tessellation, or "representational art" tessellation. In that kind of tessellation, each "tile"-- each repeating shape-- looks like a real thing. Escher didn't invent that kind, but he did reinvent it and popularized it in Western culture.

The other kind of tessellation is much, much older and more widespread. It's often called Islamic tessellation, or geometric tessellation, or Alhambra style, or non-representational tessellation..or just abstract tessellation.

It's worth noting that Escher, the most famous tessellator of tiles shaped like "real things", drew his inspiration from other kinds of tessellation. He recognized geometric tessellations in chemistry, geography and biology. He also drew heavy inspiration from an Islamic-style palace called "Alhambra" in Granada, Spain. The decorative tessellations of Alhambra are very beautiful...even awe-inspiring... to artists and mathematicians.

For simplicity's sake, let's call the two kinds of tessellation "Escher style" and "Abstract style", though we could just as rightly call them "representational" and "Geometric", or "things" and "geometric shapes", or "Escher" and "Islamic".

The original webmaster of, Dr. David Annal, preferred to post only Escher-style tessellations. I think he felt, as I do, that tessellations which look like "real things" such as people, cats, and toasters require the artist to do a lot of tweaking of the tile shape. To us, this's proof that the artist invested time and thought, and had a goal-- a theme-- in mind. Simply geometric or abstract designs have no such requirement, and so (David thought) they might require less effort from the artist. If your tile shape looks like a random blob or a piece of chicken wire, how can we know that you worked hard on it to make it look juuuuust right?

However, I've had a change of heart. Two years ago a Muslim person wrote to me from the Mid-east, asking why my site didn't show Islamic/Alhambra/Abstract style tessellations. He reminded me that

  • Islamic-type tessellations predate Escher's type-- in fact, the ones at Alhambra inspired Escher.
  • Islamic-type (geometric) tessellations are, when done ...ummm... artfully, are quite beautiful in their own way. They have a sense of math and balance and harmony.
  • It would be a little unfair, even possibly religous bigotry, were I to reject art simply because the artist's religion insists that its artists never portray "real things". Both kinds of tessellation are beautiful, aren't they.

Why did I mention religion? Well, some religions, particularly in the Judaism-Christianity-Islam line, prohibit images of "real things" for the simple reason that people might start to worship the images (like in the story of the golden calf in the torah/bible/koran) instead of that religion's god. The art might become an idol. When you see how much the painting of Mona Lisa or the Statue of Liberty or the ceiling of the Sistene Chapel earn peoples' awe, you can sort of understand the point.

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, 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, our current decision is to allow Abstract/Geometric/Islamic/Geometric 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 that type. 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 I 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 non-representational tessellation are a bit vague, but I hope I've given you some sort of guide so you can predict which art I'll want to accept.

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Escher style:
tiles shaped like real things

Abstract / Islamic / Alhambra style:
tiles that don't look like real things

Actual Alhambra  tesellation tilings