Anne Burns

Professor of Mathematics
Long Island University
Brookville, New York USA

Almost all of my computer-generated art is a result of a recursive process. I am fascinated by recursion and the complexity that can be achieved by repeatedly applying a simple transformation to an initial object and changing the parameters at each stage. I am inspired by patterns that appear in nature.

Circles on Orthogonal Circles
Circles on Orthogonal Circles
12" x 16"
Digital print

A loxodromic Möbius transformation has two fixed points, one attracting and the other repelling. Starting with a small circle around the repelling fixed point and repeatedly applying the Möbius transformation results in a family of circles that grow at first, each containing the previous one. Successive images eventually pass over the perpendicular bisector of the line connecting the fixed points and shrink down as they are attracted to the other fixed point. Each circle in a second family of circles passes through the fixed points and is mapped to another circle in that family. Each circle in the second family is orthogonal to every circle in the first family.