Kerry Mitchell
My work is composed primarily of computer generated, mathematically-inspired, abstract images. I draw from the areas of geometry, fractals and numerical analysis, and combine them with image processing technology. The resulting images powerfully reflect the beauty of mathematics that is often obscured by dry formulae and analyses. An overriding theme that encompasses all of my work is the wondrous beauty and complexity that flows from a few, relatively simple, rules. Inherent in this process are feedback and connectivity; these are the elements that generate the patterns. They also demonstrate to me that mathematics is, in many cases, a metaphor for the beauty and complexity in life. This is what I try to capture.
This piece is a fractal image based on the Julia set of z = z^2-2. However, at each step, the iterate z is rounded to the nearest Gaussian integer and transformed using the tan(z) function. The image is colored according to the polar angle of the sum of the residuals (iterate minus the rounded value). The Julia set gives rise to the lemniscate curve, representing the symbol for infinity, and the roughness of the rounding and transformation suggests a continuing construction process.
This image is a Julia set using the formula z = c sin(1/z). It was rendering by the mean of the ratio of imag(z)/real(z) (arctangent of the polar angle). The hard black and white edges were created by exploiting the branch cut in the polar angle calculation at pi.