When playing the chaos game normally, we roll a die and select an anchor point and go halfway between the previous point and the random anchor point.

But we don't have to only go precisely halfway to the new point. We can vary that ratio.

The images in the previous section were all generated with a ratio of 0.5.

This shows varying the ratio smoothly from 0.01 up to 0.8. At values above 0.5, then the structure escapes the bounds of the anchor points.

If we had enough data points, we would still see the Sierpinski triangle. The render time increases dramatically with more points, though.

We can see if the other polygons produce more interesting structures with different ratios.