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.
Begin with a polygon defined by an ordered list of points in the plane. Then, iterate by creating new polygons, the vertices of which are the average of two subsequent vertices from the previous polygon. In the limit of infinite iterations, the vertices lie on an ellipse. This image shows the process at a series of intermediate steps. 2500 random points were chosen as the initial vertices, which were then iterated between 40 and 60 times. Also, the number of points averaged together ranged from 60 to 40 (each curve shows a different number of iterations and of averaged points). Mathematically, this image differs from the companion piece, "Iterated Polygons 1" only in the random number function seed.
Begin with a polygon defined by an ordered list of points in the plane. Then, iterate by creating new polygons, the vertices of which are the average of two subsequent vertices from the previous polygon. In the limit of infinite iterations, the vertices lie on an ellipse. This image shows the process at a series of intermediate steps. 2500 random points were chosen as the initial vertices, which were then iterated between 40 and 60 times. Also, the number of points averaged together ranged from 60 to 40 (each curve shows a different number of iterations and of averaged points). Mathematically, this image differs from the companion piece, "Iterated Polygons 2" primarily in the random number function seed used.