FractionalGeometry-Chap2

Some understanding of the geometry and topology of

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Unformatted text preview: (b) Q1 Q2 P1 Figure 2.48: Points for Prob. 2.7.6 (left) and Prob. 2.7.7 (right). Prob 2.7.8 Use the method of this section to find the IFS parameters for the three spirals of Fig. 2.37. If your answers differ from those found in that section, comment on possible sources of the differences. Prob 2.7.9 Use the method of this section to find the IFS parameters for (a) the ferns of Fig. 2.43 (b) the spirals of Fig. 2.44 (c) the spirals of Fig. 2.45 (d) the snowflakes of Fig. 2.46. 2.8. VIDEOFEEDBACK WITH MIRRORS: ANALOG IFS 2.8 83 Videofeedback with mirrors: analog IFS Although usually taken as an illustration of dynamical processes, with several mirrors videofeedback can give rise to stable fractal patterns. This is a happier role for mirrors than that assigned by Borges: “For one of those gnostics, the visible universe was an illusion or (more precisely) a sophism. Mirrors and fatherhood are abominable because they multiply and disseminate that universe.” (Tl¨n, Uqbar, Orbis Tertius in [18]). o The left side of Fig. 2.49 shows the...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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