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Fractals and the Koch Snowflake

by Elizabeth Klenk

Elizabeth Klenk

on 29 July 2012

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Transcript of Fractals and the Koch Snowflake

Fractals and the Koch Snowflake By Elizabeth Klenk ``A set with its Hausdorff-Besicovitch dimension strictly greater than its topological dimension." - B. B. Mandelbrot. What is a Fractal? For a Fractal F: F has a fine structure. F is often self-similar to some extent. F is too irregular to be described by classical geometry or calculus. F normally has a Hausdorff dimension greater than its topological dimension. Self-Similar Fractals Similarity Dimension: For any self-similar fractal set, where N is the number of self-similar pieces which the fractal is composed of and r is the scale factor of such parts, the dimension D is given by, D=log(N)
log(r) The Koch Snowflake Niels Fabian Helge von Koch Construction Construction Construction
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