FractionalGeometry-Chap2

Example 271 ane transformation parameters from point

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Unformatted text preview: you will change the rules to address those problems. Repeat until you are satisfied with the picture. (a) a leaf, (b) a cloud, (c) a mountain range, (d) broccoli, (e) a starfish, and (f) a caricature of a face. (A surprisingly effective example of this was done by a student in 1993.) 2.7 Finding affine transformations from point images In the last section we saw how to estimate the parameters for IFS that generate forgeries of natural objects. While some simple relatives of the gasket, especially those involving both reflections and rotations, can be a bit challenging, still they are relatively clean. Natural fractal IFS can involve affinities (r = s) or 78 CHAPTER 2. ITERATED FUNCTION SYSTEMS distortions (θ = ϕ), not so easy to parse visually. So in this section we develop a more mechanical, procedure. Here we need only locate the images of selected points, not try to identify transformed copies of the whole shape. Specifically, take three easily identified, non-collinear points in...
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