Fun with Sierpinski Pyramids

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Presentation transcript:

Fun with Sierpinski Pyramids Dylan Bland EPS 109 December 1, 2011

Instead of infinite removal… “Chaos Game” method: Fractal pyramid: Hausdorff dimension: log(5)/log(2) = 2.3219 Each pyramid replaced by 5 pyramids, twice smaller Instead of infinite removal… “Chaos Game” method: Fractal is created iteratively creating a sequence of points, in which each point in the sequence is a given fraction of the distance between the previous point and one of the vertices of the triangle Also an IFS --- Iterated Function System Total of 5 transformations with an equal chance of happening, one for each side of the pyramid

Sierpinski Movie