FractionalGeometry-Chap2

A surprisingly eective example of this was done by a

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Unformatted text preview: r 0.40 0.50 1 s θ ϕ e f 0.40 0 0 0 0 0.20 0 0 0.5 0 1 π/3 π/3 0 0.7 IFS for the left snowﬂake of Fig. 2.39. prob 0.04 0.04 0.92 The right snowﬂake of Fig. 2.39 is generated with the table below. Note the 74 CHAPTER 2. ITERATED FUNCTION SYSTEMS change in T2 and the additional transformation. Are the roles of these changes clear? r 0.40 0.50 0.30 1 s θ ϕ e f 0.40 0 0 0 0 0.20 0 0 0.5 0 0.30 0 0 0.8 0 1 π/3 π/3 0 0.7 IFS for the right snowﬂake of Fig. 2.39. prob 0.03 0.03 0.03 0.91 This is, of course, just the simplest of beginnings. Experiment with the software and see what you can ﬁnd. Practice problems Prxs 2.6.1 Find IFS rules to generate the spiral on the left of Fig. 2.41. Prxs 2.6.2 Find IFS rules to generate the spiral on the right of Fig. 2.41. (b) (a) Figure 2.41: Fractals for Prxs 2.6.1 (left) and Prxs 2.6.2 (right). Practice problem solutions PrxsSol 2.6.1 For the reference line in th whole spiral we take OA and measure its length as 3 cm. The corresponding le...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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