Thoughts on Maurits Escher

Escher is probably best known for his three dimensional optical illusions, such as the ever-descending staircase. But close behind are the tiling images, where the tiles are typically animals and their perfect interlocking shows a high degree of novelty.

With my interest in Geometry and Art, Escher's tiling images were an obvious target.

The image reproduced here is called Square Limit.



The fish that appears in the many locations in the image is identical (apart from size, orientation, sense and colour) everywhere it appears. Escher's remarkable talent was to design realistic looking animals with this sort of interlocking property.

Some would say this isn't Art. But few would say it isn't interesting.

Most of Escher's later tiling works have interesting Geometrical properties. Working out how to recreate them digitally is a challenge. I have spent may hours (over many years) perfecting the description of Square Limit, in a form that the computer can interpret.

It transpires that the description is in fact fairly trivial. As Escher no doubt knew.

The tiling-plan that Escher used, reproduced here, has the amazing property that the individual fish only fit the pattern in one way. Once one has placed a single fish anywhere on the tiling-plan, there is only one way to place every other fish if they are all to interlock correctly.

What is even more amazing is that the image (and the tiling-pattern of course) are infinite. Regressing towards the edge of the image in ever-decreasing triangles.

One can only ever draw a finite part of that image, of course. And add a vague impression of the miniscule omitted elements.