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

Chaos Game Exploration of Triple Vertex Polygons

John Paul, Thomas, BjornGUTS/Challenge STI 2009

Chaos Game

Method of describing a fractal patternOR 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.

The Math

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 iterated function series.

Whenever x0 belongs to the attractor of the IFS, all iterations xk stay inside the attractor and.

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?

Results

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

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

Results Cont’d

Expanding the Model/Project

Pull the mathematics out of the equation:

Jonathan Wolfe, HELP ME!

References

Wikipedia!

http://en.wikipedia.org/wiki/Chaos_game

http://en.wikipedia.org/wiki/Sierpinski_triangle

Bennett, N. NetLogo Mystery Model.