My Tesselations

I remember working with tesselations in high school, but mostly I would conceive them and stop at a rough sketch. Now that I have vector graphics programs, it's easier to finish them.

[Angry dog tesselation]

This was my first attempt to illustrate a finite geometry in which everything shrinks as it moves away from the center of the universe, such that it looks to its inhabitants just like an infinite Euclidean plane. The transformation I implemented here was more like a perspective view of a sphere on which the tiles had been laid.

[Monkey tesselation]

This was my second attempt to illustrate such a geometry, and I got it right this time. The monkeys think that they occupy an infinite plane, but they are deceived. I used this illo in my dissertation. (Jan 2002)

I am aware that these aren't perfect tesselations, since there are gaps between the tiles. My excuse is that I was using the repeating pattern of dogs or monkeys to illustrate a point about the underdetermination of geometry; the tiling was incidental. Nevertheless, I would have been happier if I could have eliminated the square gap between each cluster of dogs.

[Reid tesselation]

This is the tesselated bust of Scottish philosopher Thomas Reid. I decided to draw it after looking at the medallion portrait and noticing that it could very nearly fill the plane in its original shape. (Nov 2002)