FractionalGeometry-Chap2

Given three non collinear points the initial points

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Unformatted text preview: ngth in the lower right subspiral is CA, having length 0.8cm. This subsprial is similar to the whole spiral, so for it r = s = 0.8/3 = 0.27. The corresponding lines DE , F G, and HI all have length 0.8 cm, so all four corner subspirals have r = s = .27. Removing the corner subspirals, OB corresponds to the reference line. Because OB has length 2.3 cm, for the middle piece of the spiral, r = s = 2.3/3 = 0.77. Because CA and F G are parallel to OA, the lower right and upper left corner subspirals are not rotated. The middle spiral is rotated by ∠BOA = 30◦ . Because DE and HI are parallel to OB , the lower left and upper right spirals are rotated by 39◦ . Finally, recalling the lesson of Prob. 2.1.4, the translations for the corner subspirals can be any numbers, with appropriate signs, so long as they have the same absolute values. That is, we have the table 75 2.6. IFS FORGERIES OF NATURAL FRACTALS r 0.77 0.27 0.27 0.27 0.27 s 0.77 0.27 0.27 0.27 0.27 θ ϕ e π/3 π/3 0 0 0 1 π/3 π/3 1 0 0 -1 π/3 π/3 -1 I...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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