2019 Bridges Conference

# Tom Bates

## Statement

I have always been drawn in two directions: art, and math/science. Though my work life has been in science and software, I have strong interests in the visual arts, bronze casting, traditional printmaking, and writing. I am interested in creating images and sculptures that have a mathematical and geometric basis of some kind, yet also aim to be accessible, and possibly even beautiful, to a wider audience that might not appreciate the beauty of pure math. I enjoy writing my own software, and on occasion papers, to explore an idea or question I have, and then playing with the software to see where it can take me visually. I am often surprised by both the art and my deepened understanding that comes out of this process.

## Artworks

This image is a peek behind the scenes of the generalized chaos game. When performed on a triangle, the game produces the familiar Sierpinski gasket when the controlling "cut fraction" parameter is set to 0.5. But here the parameter value has been swept from 0 to 2 in 0.001 increments for a few thousand points. The result is a set of coupled parametric curves, with each curve being the trail of a single point coupled to its predecessor point. The Sierpinski gasket is the collection of one point from each of these curves. But the curves themselves are amazing, complex, and beautiful. Also present is a soft background glow coming from changing paths connecting the first one hundred points.
In this rather Baroque piece inspired by illuminated manuscripts, several aspects of the chaos game applied to a pentagon are shown together as the parameter controlling the game is ramped from 0.618 to 2. In the center the parent polygon glows white. Inside it is the inner fractal that occurs at 0.618 and beyond it is another fractal that occurs at 1.382. Between them, in golds and blues, are traces of points as k is ramped between these values. Finally, as the parameter goes beyond 1.382, a few point-paths are shown more prominently in oranges and yellows to illustrate the chaotic and coupled curves the point paths take beyond the outer fractal. Small fractal "coins" from several other polygon orders decorate the edges.