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:

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Grid #1

Grid #2

Grid #3

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
All images and text are ©2017 by Edward S. May unless otherwise noted. All rights reserved.