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.
Fractal shapes are easy to generate using line segments and polygons, witness the Hilbert curve and Lindemayer system shapes. Consequently, I wanted to explore images generated with iterated circles. These are generally not fractals, in the classical sense, due in large part to the lack of self similarity of a piece to the whole. Nonetheless, iterating circles can prove to be quite rewarding, aesthetically speaking.
For this image, I began with the unit circle as a base. To iterate, for each circle in the current stage, eight equally-spaced points around the circumference were found. Each point and its second neighbor (e.g., points 1 and 3, 2 and 4) formed the endpoints of the diameter of a newly-defined circle. This image represents a magnification of the fifth level of iteration, rendered by simply drawing the outlines of each of the circles.
Fractal shapes are easy to generate using line segments and polygons, witness the Hilbert curve and Lindemayer system shapes. Consequently, I wanted to explore images generated with iterated circles. These are generally not fractals, in the classical sense, due in large part to the lack of self similarity of a piece to the whole. Nonetheless, iterating circles can prove to be quite rewarding, aesthetically speaking.
For this image, I began with the unit circle as a base. To iterate, for each circle in the current stage, n equally-spaced points were found, where n was a multiple of five. Each point was the point of tangency of a new circle, inside the parent circle with half of its radius. To create the image, I colored each pixel by how many times it was in the interior of a circle on the first iteration. Nineteen such layers were combined, for values of n from 10 to 100, inclusive.
Fractal shapes are easy to generate using line segments and polygons, witness the Hilbert curve and Lindemayer system shapes. Consequently, I wanted to explore images generated with iterated circles. These are generally not fractals, in the classical sense, due in large part to the lack of self similarity of a piece to the whole. Nonetheless, iterating circles can prove to be quite rewarding, aesthetically speaking.
For this image, I began with the unit circle as a base. To iterate, for each circle in the current stage, determine 12 equally-spaced points around the circumference. Adjacent points were taken in pairs, each pair forming the endpoints of the chord of a newly-defined circle. To create an image, I simply drew each circle in the second iteration. For added interest, I overlaid 16 sets, with each set being defined by the angle that the chord subtended in the new circle.