FractionalGeometry-Chap2

# FractionalGeometry-Chap2

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Unformatted text preview: 2.1.8. Prob 2.1.7 Find IFS rules to generate the fractals of Fig. 2.12. Each is enclosed in the unit square with the origin at the lower left corner. Prob 2.1.8 Given the initial image, the unit square containing an L, on the left side of Fig. 2.13, ﬁnd the IFS rules for which the image on the right side of that ﬁgure is the second iteration of this IFS. 2.2 The Hausdorﬀ metric To begin the proof of convergence of the IFS process, illustrated by cats turning into a gasket in Fig. 2.3, we need a way to measure the distance between compact subsets of the plane. Distance between points is clear from Pythagoras. In calculus, by the distance between curves we mean the shortest distance between the curves. With this understanding of distance, note that the circles C1 given by x2 + y 2 = 1, and C2 given by (x − r)2 + y 2 = (1 + r)2 are the same distance, 0, apart, for all r ≥ 0. Visually, C1 and C2 look much more alike for small r than for large. However we measure the distance between these c...
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## This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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