FractionalGeometry-Chap2

By making the shrinkings anities instead of

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Unformatted text preview: Often natural fractal forgeries involve transformations for which r = s or θ = ϕ. Determininging these parameters by visual inspection can be challenging; in Sect. 2.7 we present an alternative: selecting three noncollinear points in the whole set, all six transformation parameters can be found from the coordinates of the images of these points in each scaled copy of the set. But in many instances, parameterscan be approximated adequately by visual inspection. Here we use this approach for the tree and fern, and a few other examples. Figure 2.33: Left: fractal tree. Right: fractal fern. The tree rules are relatively simple. We assign approximate probabilities for rendering by the random IFS algorithm. 68 CHAPTER 2. ITERATED FUNCTION SYSTEMS r 0.60 0.50 0.50 0.50 0.05 0.05 s 0.50 0.45 0.55 0.40 0.60 -0.50 θ ϕ e f 40◦ 40◦ 0 0.60 20◦ 20◦ 0 1.10 -30◦ -30◦ 0 1.00 -40◦ -40◦ 0 0.70 0 0 0 0 0 0 0 1.0 IFS for the tree of Fig. 2.33. prob 0.20 0.20 0.20 0.20 0.10 0.10 The first four rules make the lower left, uppe...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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