FractionalGeometry-Chap2

qn the distance is dt1 tn q1

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Unformatted text preview: , or are some pieces missing? Can this explain any discrepancies between your IFS image and the videofeedback image? Prob 2.8.1 Refer to the videofeedback images of Fig. 2.52. Prob 2.8.2 Refer to the videofeedback images of Fig. 2.53. (a) (b) Figure 2.52: Videofeedback images for Prob. 2.8.1 (a) (b) Figure 2.53: Videofeedback images for Prob. 2.8.2 86 2.9 CHAPTER 2. ITERATED FUNCTION SYSTEMS Some topological questions about IFS attractors Solving the inverse problem for IFS, that is, finding IFS rules with attractor approximating a given compact set, can be viewed as a search (usually very far from random) through IFS rule space. Some understanding of the geometry and topology of rule space could guide our search. To begin, what can be said about the range of the individual parameters, r, s, θ, ϕ, e, and f , if the transformation is a contraction? Being translations, e and f have no effect on contractivity. Before moving on to the other parameters, recall from Prob. 2.1.4 that multiplying all the ei and fi of an IFS by a factor w changes the...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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