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FractalsBeauty in Numbers & Infinity

Title SlideFractals beauty in numbers and infinity1

fractusbrokenfractured

Intro 1The word fractal comes from the Latin word fractus meaning broken or fracturedA fractal is a mathematical concept that allows for the geometrical representation of objects and patterns whose shapes are irregular, rough, intermittent, and complicated.

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Intro 2Fractals are also characterized bySelf-similarityInfinite resolutionBranching patternsMathematically they are everywhere continuous, but nowhere differentiable4

Z z2+c

Math 1Fractal geometries rely on simple addition and multiplication.Each location on the 2D plot is given an unique initial z-valueEvaluating the right side of the formula produces a new z-valueThe process repeats as this new z-value is then plugged back into the right side of the equation, and evaluated to produce yet another new z-value6

Math 2As the iterations continue, the z-value will approach either zero or infinityIf z goes to zero, then that coordinate is filled in blackIf z goes to infinity, then that coordinate is given a color; the color is determined by the speed with which z approaches infinity8

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Math 2As the iterations continue, the z-value will approach either zero or infinityIf z goes to zero, then that coordinate is filled in blackIf z goes to infinity, then that coordinate is given a color; the color is determined by the speed with which z approaches infinity9

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Math 2As the iterations continue, the z-value will approach either zero or infinityIf z goes to zero, then that coordinate is filled in blackIf z goes to infinity, then that coordinate is given a color; the color is determined by the speed with which z approaches infinity10

dic.academic.ru/.../70/Fractal_Broccoli.jpg

Fractal Character & in Nature(narration continues over next slides)Fractals have valuable characteristics beyond those of infinite resolution, and infinitely varying patternsIts been said that fractals have a very organic feel to them. Their shapes and patterns might remind us of bugs, tree branches, lightning bolts, or other things found in nature that have very recognizable shapes, but are still not easily described using Euclidean Geometry alone.Fractals may be the new language of science and nature, where the path of a lightening bolt or the structure of a human brain could be described with a few simple fractal formulas

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Photo: Jeffrey Meyer

Fractals in Nature tree branches14

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1.bp.blogspot.com/.../Earths_Fractal_Brain_2.jpg

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The universe is full of fractals. Indeed it may even be one.Ian Stewart

Produced by: Jeffrey MeyerFractals generated using ChaosPro SoftwareReef Nebula, by Moonchilde-Stock on deviantArt

CreditsThe universe is full of fractals. Indeed it may even be one. Ian Stewart

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