...and a bit of autobiography

Like Hop David, I was around 40 when I tried my first Escher-like tessellation. From age 10 onward, I'd loved M. C. Escher's hyperrealism and trick perspective, but I didn't really like tessellation. Around age 42, though, I Googled for Escher art contests, and found that the only fairly large Escheresque contest was for tessellations. I drew a patternless ramble that didn't really work, scrapped it, and then drew "Bootlickers", which won that year's World of Escher contest.

At first, I got headaches thinking about manipulating opposite edges of an object. It felt exactly like stretching a leg muscle or jogging after a long period of not exercising...except that the muscle was in my head, and no amount of soft sneakers would help.

Nowadays, creating a tessellation is much easier because I've learned a few helpful shortcuts and cheats.

Sitting Buddha

First among the shortcuts is how to start. I familiarize myself with a few basic shapes that I know will tessellate: bricks, triangles, hexagons like chickenwire.

Second, I look around for objects that roughly fit one of those shapes. For example, a sitting cat is roughly triangular, so stacking cats makes a good tessellation. Can you also see that a buddha sitting Indian-style is roughly triangular?

Sitting Buddha Tessellation showing triangle origin
Can you see the relationship between these shapes & triangles? Can you see the blue-and-green buddhas? 

Notice that flips, rotations, and translations are all OK.

A "flip" is what you see when your basic shape is mirrored: one cat faces left, and the cat next to it is identical except that it faces right, like a mirror reflection of the first cat.

A rotation is when you use the same basic shape all around your pattern, but in some places it's spun around a point. The perfect example would be slices in a round pizza: together they tessellate; they're all the same shape; their only difference is that each one is rotated a little compared to the ones around it.

A translation is when you slide your basic shape a little to the left/right, or up/down. The perfect examples are brick walls and chicken wire.

By taking the basic shape and spinning, pushing left or right, or taking mirror images of it, you can get a lot of tessellation options. The 17 combinations of ways that you could spin, push, or flip your basic shape is together called the set of "17 wallpaper groups".

Third, decide whether that tessellation is worth developing, I look for a lot of flexibility in the outline. For example, it's pretty easy to manipulate the outline of a person in big floppy clothes, but the outline would be far less flexible if the person were wearing Spandex (tm) or knights' armor. So, our cat will get long hair, and our sitting Buddha will get big floppy robes and some kind of random long hair.

"Flexibility" can also mean a forgiving nature, or just using a shape that people don't know very well. For example, fishes' big floppy fins give you a valuable forgiveness no matter what liberties you take. Not only are those fins and body and tail ready to be twisted all around, but it's a rare expert who can say for sure whether you've accidentally left off a fin, or made the tail too big, or put a grouper's mouth on a guppy. Take a look at the red and grey fish tessellation at right. Notice that the artist, Escher, took wild liberties with the shape of the tail and every fin on the fish.

For some animal species and clothing fashions, you can break most of the rules of anatomy and not expect the audience to notice: put a nut-eater's beak on an eagle, leave off the legs, and nobody notices! Notice for example that in this bird tessellation, we're ready to accept it as a bird when there are no feet, and only a vague diamond-shaped suggestion of wings and a body.

You can't do that with well-known rigidly shaped species like elephants, horses, dogs, and deer. You can't expect to make big changes in well-known animals: distortion the length of the legs, missing or misplaced legs, horns on bunnies, and antlers on elephants are soon spotted by the clever half of your audience. ;-)

The most flexible animals you can work with are: birds, lizards, fish, and people in floppy clothes. If you did a quick survey of tessellations, you'd notice that these subjects are overrepresented.

The last step is to mentally work out where concave parts will line up with convex parts, as you line up the borders of adjacent cats, buddhas, fish, or whatever. There are no shortcuts here, except to figure it out in your heard or use a light grey pencil, a big eraser, and two sheets of tracing paper.

Ta-da-a-ah, the tessellation's done, except for scanning, copying, and pasting to duplicate the object which you've chosen to tessellate.

Let me offer a pair of hints on presentation:

Use strong thick borders between objects, and strongly contrasted colors on adjacent objects so it's immediately apparent where one object ends and the next begins.

Don't just draw a perfect pattern with endless repetition. Perfect repetition is perfectly BORING.

Instead, pull one object out of the pattern, and make it look goofy. Or, have the tessellating objects along one border float apart or fade into the background. Or have objects morph from one tessellation to fish along one side of the picture gradually changing to simple diamond shapes in the center of the picture, and then changing shape to become birds along the far edge of the picture.

You know these shapes will tessellate:
brick tessellation

The Triangles of Madison County

chicken wire hexagons

escher fish tessellation
One of Escher's Fish Tessellations

swan tessellation by CarouselOfLife at DeviantArt
This is only barely like a bird, but it's OK.

goofy fish tessellation
Goofy is good. Perfect repetition is boring