Some experimentation with Chaos Game.

For those unfamiliar with Chaos Game, it's a mathematical experimentation (not really a "game") which applies some constraints to randomness, so order and pattern will emerge from it.

For example: you have an equilateral triangle and you start at the topmost vertex of it. You randomly choose between the three vertices, then you place a point exactly in the middle between the current coordinates and the chosen vertex. You repeat the process indefinitely, choosing another vertex and placing a point midway between the current coordinates (it's now a place inside the triangle) and the chosen vertex. Gradually, you'll start to notice a pattern, in this exact case, you'll end up with a Sierpinski triangle.

The more random and unbiased the randomness, the more quality the end result will have.

You can change parameters. For example, you can change the geometrical shape (e.g. a pentagon instead of a triangle), or you can change the ratio (i.e. how far from the current coordinate to the next coordinate: instead of going half the way, you can choose to go 1/3 (0.3333...) of the way, or you can even extrapolate past the next coordinate with a ratio bigger than 1). You can choose to not repeat the previous coordinate, or you can choose to not choose a neighboring vertex, and so on... Different constraints will result in different results, sometimes a fuzzy cloud of dots, sometimes a pattern.

It's interesting to see patterns emerging from randomness.

(I tried to send two pictures, but one of them got an error while I tried to upload...)