Chaos Game

Pick a point at random inside a regular -gon. Then draw the next point a fraction of the distance between it and aVertex picked at random. Continue the process (after throwing out the first few points). Theresult of this ``chaos game'' is sometimes, but not always, a Fractal. The case gives theinterior of a Square with all points visited with equal probability.

References

Barnsley, M. F. and Rising, H. Fractals Everywhere, 2nd ed. Boston, MA: Academic Press, 1993.

Dickau, R. M. ``The Chaos Game.''http://forum.swarthmore.edu/advanced/robertd/chaos_game.html.

Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 149-163, 1991.

Weisstein, E. W. ``Fractals.'' Mathematica notebook Fractal.m.

• Jug
• Jugendtraum
• Juggling
• Julia Fractal
• Julia Set
• Jump
• Jump Angle
• Jumping Champion
• Jung's Theorem
• Just If
• Just One
• Kabon Triangles
• Kac Formula
• Kac Matrix
• Kakeya Needle Problem
• Kakutani's Fixed Point Theorem
• Kakutani's Problem
• Kalman Filter
• Kampyle of Eudoxus
• KAM Theorem
• Kanizsa Triangle
• Kantorovich Inequality
• Kaplan-Yorke Conjecture
• Kaplan-Yorke Dimension
• Kaplan-Yorke Map