Anne Burns

Statement

I began as an Art major, but became interested in Mathematics and taught Mathematics at Long Island University for 38 years until I retired last year. In the late1980's I attended a talk on Fractals at NYU and I was hooked. After the conference I ran over to the bookstore and bought "The Beauty of Fractals". I bought a home computer whose screen resolution was 200 by 320; it had 3 colors and used floppy disks. I would program my fractals in QBasic and let the program run all night to get one picture. Over the years I learned Fortran, Turbo Pascal, Assembly Language, C++, JAVA and now I use Processing which is great. I am interested in Complex Dynamics, Applications of Complex Variable Theory, Iterative processes and recursion.

Artworks

An iterated function system is comprised of five complex functions acting on five circles; four of the circles are pairwise tangent and tangent to the unit circle and the fifth circle is centered at the origin and tangent to the other four.

This image is a zooming in on a very small region of the Julia Set of f(z) = z^2-1+ d/z(z^2-1), where d is a very small, positive real number. The Julia Set of f(z) = z^2-1 is the famous "Basilica"; adding the term d/z(z^2-1) introduces poles at 0, +1 and -1. The boundary of the set of points whose orbit escapes (the Julia Set) is made up of an infinite number of tiny decorations that resemble the decorations on the original "Basilica".

An iterated function system is comprised of five complex functions acting on five overlapping, semi-transparent circles.