What if we had more anchor points? Does every shape produce a fractal?

Chaos game played over 10,000,000 iterations with four anchor points, going halfway towards a random anchor at every iteration.

Unfortunately not.

If we have four anchor points, a square, we do simply get a random collection across a canvas.

This is because the points are free to move anywhere on the canvas with equal probability. They're not constrained to move away from any particular area.

We can see what happens with other polygons.

Chaos game played over 10,000,000 iterations with five anchor points, going halfway towards a random anchor at every iteration.

Chaos game played over 10,000,000 iterations with six anchor points, going halfway towards a random anchor at every iteration.

As we increase the number of anchor points, it doesn't seem to produce any especially interesting fractal structures. The more anchor points, the more freedom there is for points to span the entire canvas.

In the next section, we'll add some more constraints to reduce the freedom of movement.