FractionalGeometry-Chap2

For fractal c pieces b c d and e are in the same

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Unformatted text preview: tions. The position of the image of the large gap [0, 1/2] × [1/2, 1] is a clue. Pieces B and C are obtained by reflection across the y - and x-axes, respectively, followed by appropriate translations, given in IFS 2. For fractal (c), pieces B , C , D, and E are in the same orientation as the whole fractal. Pieces A and F are rotated by π , or reflected across the x-axis. With the appropriate translations, we have IFS 3. 31 2.1. ITERATED FUNCTION SYSTEM FORMALISM A F B C E C A B A (b) (a) C B D (c) Figure 2.8: Fractals for Prxs 2.1.1. r 1/2 1/2 1/2 s 1/2 1/2 1/2 θ ϕ e π π 1/2 π/2 π/2 1 −π/2 −π/2 0 IFS 1 for PrxsSol 2.1.1 f 1/2 0 1 r -1/2 -1/2 1/2 s 1/2 1/2 -1/2 θ ϕ e π/2 π/2 1/2 0 0 1 0 0 0 IFS 2 for PrxsSol 2.1.1 f 1/2 0 1 r 1/4 1/4 1/2 1/2 1/4 1/4 s 1/4 1/4 1/2 1/2 1/4 1/4 θ ϕ e π π 1/4 0 0 0 0 0 0 0 0 1/2 0 0 3/4 π π 1 IFS 3 for PrxsSol 2.1.1 f 1 1/2 0 0 1/2 1 PrxsSol 2.1.2 Because the square is taken to another square, this is a similarity transformation. That is, r = s. To find the con...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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