Beyond Escher: The Art Of Tesselation Revealed

One of the heroes of 20th century graphic art was Maurits Cornelis Escher, who used concepts from mathematics to produce extraordinary images.

One device that Escher mastered was the tesselation, which he exploited to create fantastic, periodic arrangements of images.

Today, San Le, an artist and computer programmer based in the US, shows how to generalise Escher’s technique. And his approach is so simple that anyone can give it try. “The rules to creating tiling art are straightforward,” says Le.

The idea is to study the shapes that fit together to tile a plane and to clearly label the sides that end up being adjacent. It’s then a question of creating an image that connects across these complementary sides.

The beauty of this approach is that it changes the problem from a mathematical challenge to an artistic one.

To demonstrate the power of his method, Le goes a step further than Escher by applying it to Penrose’s aperiodic tiling of a plane using darts and kites (shown above). That’s a tiling Escher never had the chance to work with but one that he would surely approve of. See below for Le’s version.

Le even goes on to show how to create fractal tilings, surely in a manner that Escher would approve of.

The results are mesmerising (see the paper for more examples). Why not give it try?

Ref: arxiv.org/abs/1106.2750: The Art of Space Filling in Penrose Tilings and Fractals