50000 Rectangles #22

50000 rectangles

(Continued from 50000 Rectangles #21.) IFS and Flame Fractals are fascinating, but they have also been done to death. I may try my hand at them someday. But for now, I just want to extract a small observation. The result of the chaos game is a random distribution. In our situation, a 2D random distribution. But one that is unlike any studied in statistics. I set up the chaos game on a set of functions, linear and nonlinear. Then use the points generated as the lower left corners of the rectangles.

The reason IFS uses contraction mapping is to ensure that the fixed set exists and is bounded. Without that restriction there may be no fixed set. The moving point in the chaos game may run off to infinity. But when using math for art, we are not so worried about such things. I mix in functions that are not contraction mappings. If they do not work, I just try something else.