FractionalGeometry-Chap2

27 the corresponding lines de f g and hi all have

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Unformatted text preview: erstood, this idea is easy to generalize to spirals with more arms. Two examples are given in the bottom of Fig. 2.37. The IFS are 72 CHAPTER 2. ITERATED FUNCTION SYSTEMS r 0.30 0.30 0.85 s 0.30 0.30 0.85 IFS for θ ϕ e 0 0 0.7 0 0 -0.7 20◦ 20◦ 0 the bottom left spiral of f prob 0 0.1 0 0.1 0 0.8 Fig. 2.37. r 0.20 0.20 0.20 0.20 0.85 s 0.20 0.20 0.20 0.20 0.85 IFS for θ ϕ 0 0 0 0 0 0 0 0 20◦ 20◦ the bottom right f prob 0 0.1 0 0.1 0.7 0.1 -0.7 0.1 0 0.9 Fig. 2.37. and e 0.7 -0.7 0 0 0 s[iral of Snowflakes are another family of shapes to which fractal characteristics often are attributed. While this statement can be criticized because of the small number of structural levels visible in snowflakes, see Fig. 2.38 from Wilson Bentley’s wonderful book [16], nevertheless, these shapes provide motivation for constructing fractal snowflakes. These are interesting because they combine rotational symmetry and scaling symmetry, and because they point out a circumstance in which the image can be rendered b...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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