FractionalGeometry-Chap2

04 092 the right snowake of fig 239 is generated with

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Unformatted text preview: ubspiral, and everything else. To help determine the scaling, rotation, and translation of the pieces, the top right of Fig. 2.37 indicates some relevant points to measure. The segment ac in the whole spiral corresponds to the segment ab in the right-most subspiral. Measuring these lengths and dividing gives the scaling factor 0.3. The corresponding calculation with the segments ec and ac gives the scaling factor 0.85 for everything else. The translation of the right-most subspiral is bc/ac = 0.7. The rotation of everything else is the angle ∠eca = 20◦ . The symmetry of the spiral suggests taking the center of the spiral to be the origin of the coordinate system. Thus the IFS for this spiral is r 0.30 0.85 s 0.30 0.85 IFS θ 0 20◦ for the ϕ e 0 0.7 20◦ 0 top spiral of Fig. f 0 0 2.37. prob 0.1 0.9 d e b c a Figure 2.37: Top Left: a fractal spiral. Top Right: this spiral with points indicated to measure scaling, translation, and rotation. Bottom: two more fractal spirals. Once und...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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