Chaos Game

lowresSierpIn the chaos game, one of a few simple rules is selected at random and applied to a point, to yield a new point. This random step is repeated over and over again, to produce an “attractor”. Here the attractor is a Sierpinski triangle.¬†Figure (i) shows the first few points, (ii) the results after 1000 iterations, (iii) the same result at a higher resolution with outliers discarded, (iv) a magnification of (iii).

What happens when you change the rules?

Here a simple chaos game is used to reveal a fractal transformation of a flower. Can you guess the rules?

 

 

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