[gus_massa]

The rest of the proof is in the Wikipedia page linked by the GP. It even has a description of the method used by the OP:

> The most common algorithm to compute IFS fractals is called the "chaos game". It consists of picking a random point in the plane, then iteratively applying one of the functions chosen at random from the function system to transform the point to get a next point. An alternative algorithm is to generate each possible sequence of functions up to a given maximum length, and then to plot the results of applying each of these sequences of functions to an initial point or shape.

[codeflo]

Are we looking at a different version of the page? I see descriptions and definitions, but no proof.