Chaos game
From Wikipedia, the free encyclopedia
The chaos game or chaosgame is a means of creating a fractal, using a polygon and a random point inside it. The fractal is created by finding the point a given fraction of the distance between the previous point and one of the vertices for a large number of times. Using a regular triangle and the vulgar fraction 1/2 will result in the Sierpinski triangle.
More generally, the chaos game is a way of generating the attractor, or the fixed point, of any iterated function system (IFS). Starting with any point x0, successive iterations are formed as xk+1 = fr(xk), where fr is a member of the given IFS randomly selected for each iteration. The iterations converge to the fixed point of the IFS. Whenever x0 belongs to the attractor of the IFS, all iterations xk stay inside the attractor and, with probability 1, form a dense set in the latter.
[edit] External links
- Mathworld Article
- Sierpinski Gasket Via Chaos Game at cut-the-knot
- IFS Fractal fern and Sierpinski triangle - JAVA applet
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