Tom Bates

Santa Barbara, California, USA
I have always been drawn in two directions: the arts and the sciences. Though my work life has been in science and software, I have strong interests in the visual arts, bronze casting, printmaking, and writing. I write my own software for creating algorithmic images. I am interested in creating images that have a mathematical and geometrical basis of some kind, yet also aim to be accessible, and possibly even beautiful, to a wider audience that may not always appreciate the beauty of pure math. I also enjoy coming across mathematical topics I feel have not been explained in a very accessible way, trying to develop a more approachable explanation, and then expressing the joy of my widened understanding through art.
The In-Betweeners
The In-Betweeners
Content and video production: Tom Bates, Soundtrack: Dylan Petrucci
This video describes and gives a small taste of the visual potential of the integer number line that arises from spiraling it around itself on square and hexagonal tessellations. Each cell of such a tessellation becomes a location to make a mark. Marks are made according to a mapping from the positive integers to another positive integer sequence.. The marks are arbitrary: they might overlap, they can be colored, semitransparent, and have any shape, but are always placed at the center of a tile in the underlying but not necessarily visible tessellation. In this case the mapping is from each of the positive integers i to another sequence such as floor[i * (n + t * ε)] where n is an integer, 0 < ε < 1, and t is an integer parameter, which can be thought of as a frame number in an animation. If t or ε were zero, this would simply map the integers to the multiples of n but when they are not I call the resulting pattern an in-betweener.