Informal Geometry Lab _19-1

# Informal Geometry Lab _19-1 - Name Informal Geometry Lab#19...

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Informal Geometry Lab #19 Fractals II Name_____________________ Partners Names___________________ Definition: A figure is self-similar if parts of the figure are small replicas of the whole figure. Definition: A fractal is a self-similar figure. Definition: A figure is strictly self-similar if any arbitrary part of the figure contains an exact replica of the whole figure. Definition: The box count of a figure is the number of boxes in a grid with at least a small portion of the figure in it. Definition: The box dimension of a figure is the slope of the best-fitting line for the points (log 10 (x), log 10 (y)) where x is the total number of boxes in the box count grid and y is the box count of the figure. Definition: The similarity dimension of a self-similar fractal shape from line segments is log ( ) log ( ) 10 10 N r , where N is the number of smaller line segments replacing a larger segment at each iteration, and r is the amount any segment is longer than each of the segments at the next stage. Definition: The fractal dimension of a strictly self-similar fractal is the limit of the box dimension as n approaches infinity, which also equals the similarity dimension. So fractals frequently have fractal dimension that is not an integer.

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## This note was uploaded on 05/11/2008 for the course MATH 101 taught by Professor Dechene during the Spring '08 term at Fitchburg.

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Informal Geometry Lab _19-1 - Name Informal Geometry Lab#19...

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