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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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