TURBO MODE! IMPORTANT: This will make more sense if you read the notes. Also, check out this link: http://mathworld.wolfram.com/ChaosGame.html Press Space (or Flag) to start. Press S to show/hide variables. Press R to randomize variables and start over. Press T to randomize all variables but points per side. Number of Sides is the number of sides of the polygon. Numerator is the numerator of the distance the point moves at each step. Denominator is the denominator of the distance the point moves at each step. Number of Sides changes whether there are just (Number of Points) points or whether there are more per side. For example: If you change this to 1 and put Number of points to 4 and Numerator to 2 and Denominator to 3, you get Sierpinski's Carpet.
Ailurophile23 asked my assistance to increase the speed on his/her Chaos Game fractal-rendering project. This is the result. CURATED!!! 2-17-14 Thanks to @The_Grits.