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# Chaos Game

Chaos game is a mechanism for generating an approximation of a fractal. You determine the vertices of a polygon, and then randomly generate a point inside of that polygon.

For an arbitrary number of steps, you move the point halfway between its current location and a randomly chosen vertex. That point is colored in, and you repeat the process as much as desired. Some chaos games, known as restricted chaos games, have requirements for a randomly chosen vertex's relation to the previous one.

If you want to make chaos games with custom shapes, go here.

**Click on a square to begin the chaos game for that pattern, and click on it again to stop it.**

## Triangle, No Rules

The fractal that this approaches is the Sierpinski Triangle, which has a cleaner render here.

## Square, No Vertex Twice in a Row

If the chaos game is played with a square with no rules, the entire space will be filled up. For a meaningful fractal to be established, rules must be set.

## Square, No Diagonal Vertices

## Pentagon, No Rules

## Pentagon, No Vertex Twice in a Row

## Pentagon, No Vertices Immediately Clockwise

## Pentagon, No Vertices Immediately Adjacent

## Pentagon, No Vertices Two Away