FractionalGeometry-Chap2

Is the blue part of this coloring scheme the union of

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Unformatted text preview: ement of the four transformations. Right: the attractor witout rotations or reflections. Exercises Prob 2.9.1 In Example 2.9.1 find a value of θ1 = ϕ1 slightly larger than π/4 so the attractor is connected. Prob 2.9.2 Modify Example 2.9.1 in this way r 1/2 1/2 1/2 s 1/2 1/2 1/2 θ ξ −ξ 0 Table for ϕ ξ −ξ 0 the IFS e 0 1 − cos(−ξ/2) 1/4 of Prob. 2.9.2. f 1/2 − sin(−ξ/2) √ 3/4 Certainly, for ξ = 0 the attractor is an equilateral gasket. Find another value of ξ for which the attractor is an equilateral gasket. Is it the same size as the ξ = 0 gasket? Prob 2.9.3 Using the four function placements of the practice problems, find a four function IFS with hybrid attractor. Probs 4 – 7 use a four function IFS, three scaling by 1/2, one scaling by 1/4, placed according to the schematic on the left side of Fig. 2.62. As in example 2.9.2, the each transformation can involve reflection across the x-axis, reflection across the y -axis, or rigid rotation by π/2, π...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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