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Chaos Game Exploration of Triple Vertex Polygons John Paul, Thomas, Bjorn GUTS/Challenge STI 2009

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Chaos Game Method of describing a fractal pattern OR attractor of an iterated function set. Agents hop around randomly on the surface, instead of traditional methods of testing to see whether each iterated function is a part of the fractal (i.e. cutting). Coined by Michael Barnsley.

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The Math Starting with any point x 0, successive iterations are formed as x k+1 = f r (x k ). Where f r is a member of the given IFS randomly selected for each iteration. The iterations converge to the fixed point of the iterated function series. Whenever x 0 belongs to the attractor of the IFS, all iterations x k stay inside the attractor and.

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The Model Start with original Serpinski Chaos Game code (written by Nick Bennett) What happens when we vary the factor? I.E. Instead of ½, how about.23 or.75?

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Results

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http://en.wikipedia.org/wiki/File:Sierpinski_pyramid.png

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http://en.wikipedia.org/wiki/File:Sierpi%C5%84ski_Pyramid_from_Above.PNG

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Results Contd

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Expanding the Model/Project Pull the mathematics out of the equation: Jonathan Wolfe, HELP ME!

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References Wikipedia! http://en.wikipedia.org/wiki/Chaos_game http://en.wikipedia.org/wiki/Sierpinski_triangle Bennett, N. NetLogo Mystery Model.

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