Grid Mapping Fractals

The algorithm which I call "grid mapping" is simple and straightforward, and produces fractals quickly on a PC. The programs which created these images were written in QuickBasic.

Subdividing the Colors

The process of grid mapping begins with a "monad", a square of a single color, which is subdivided progressively, to a limit set by the user. The resulting grids are 2x2, 4x4, and so on, as shown below.

......

Each possible "monad" color is mapped onto a 2x2 grid of four possible colors. Suppose we used the following mapping rules for the three colors shown:

Back to Fractals        Back to Chromatism
 
Grid #1
Grid #1
Grid #2
Grid #2
Grid #3
Grid #3
Grid #4
Grid #4

If we initialize the image with a blue monad, the mapping would begin as follows:

......

At each level of subdivision, each color uses its mapping rule to generate the four colors of the next subdivision. Note that blue has reappeared at the third level: the process will repeat itself in those squares, thus creating the necessary conditions for a fractal object: recursion and self-similarity.


Grid Mapping Fractals

Last Updated November 18th, 2001
Web Page by Ned May (nedmay@chromatism.net)
URL http://chromatism.net/chromat/spirals.htm
All images and text are ©2001 by Edward S. May unless otherwise noted. All rights reserved.