FractionalGeometry-Chap2

FractionalGeometry-Chap2

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

Ask a homework question - tutors are online