# Tom Bates

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 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 may not always appreciate the beauty of pure math. I write my own software for creating algorithmic images. I enjoy both writing the software to explore some idea or question I have, and then playing with it to see where it leads visually. I am often surprised by what comes out of this process.

A collection of several integer sequences marked on hexagonal-spiraled number lines. The central solid blue hexagon in the lowest row has every integer marked. The hexagon in the middle of the image is the result of marking the multiples of two, and the top hexagon is generated by marking the multiples of three. All the others are “inbetweeners” in that the marked sequence is a mixture of the monotonic sequences of the multiples of 1, 2, or 3, giving rise to many unusual patterns.

All the marks are tiny blue hexagons. Where no marks were placed, either the background color has bled into the hexagon, or magenta has been used to color unmarked areas wholly surrounded by blue marks.

A collection of nine integer sequences on square-spiraled integer number lines. In each square the mapping is I → Y: f(i) = floor[i * s], where I is the set of positive integers plus zero, and s is one of {17, 18.75, 20.5, 22.25, 24, 25.75, 27.5, 29.25, 31}. The central, upper left, and lower right squares have s = 17, 24, and 31, yielding the patterns formed by their multiples on a square spiral. The other five patterns are “inbetweeners” in the sense that they show patterns that appear in between pure multiple patterns as the floor operator causes non-integer values of s to generate wild mixtures of two integer sequences.

All the marks are semi-transparent colored dots, expanded to slightly overlap any marked nearest neighbors.