Fractals from Voronoi diagrams

A Voronoi diagram is created from a set of points by dividing the plane into regions, where each region consists of the area closest to one of the points.

To create a fractal, first create a Voronoi diagram from some points. Next, add more points and create new Voronoi diagrams inside each original Voronoi region. Repeat the process recursively. The following figure illustrates this process. Recursive Voronoi diagram

The following image shows the leaf-like structure that can be created by this technique. Recursive Voronoi diagram

If the points are distributed in a circle, a fractal such as the following can be created. Recursive Voronoi diagram

For more details, see my paper on how to generate fractals from Voronoi diagrams. This paper was published in Computers & Graphics, 17(2), Mar. 1993, pp 165-167. My Voronoi fractals also appeared in the book Chaos and Fractals: A Computer Graphical Journey.

If you're looking for Voronoi source code, please look at this site.

Ken Shirriff:
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Copyright 1998 Ken Shirriff. Last updated 1/5/99.