Chapter 4 - Generating fractals from Voronoi diagrams

Abstract

Voronoi diagrams can be used to generate interesting fractal patterns that resemble leaf veins, roadmaps, and cracked pottery glaze. The patterns are generated by recursively creating a Voronoi diagram inside each Voronoi polygon. A Voronoi diagram consists of nearest-neighbor polygons. To generate the fractal images, one starts with a small set of points and draws the Voronoi diagram of these points. Then, a denser set of points is used and a new Voronoi diagram is computed inside each region of the first diagramFor each region only the points inside that region are considered, and a Voronoi diagram is drawn clipped to that region. This process is repeated recursively, building a new Voronoi diagram inside each region of the higher-level diagram. The output can be varied in several ways. The most obvious parameters are the number of points at each level and the total recursion depth.