FractionalGeometry-Chap2

Figure 265 coloring schemes for prxs 2101a left and

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Unformatted text preview: , or 3π/2. Translations place each image in the appropriate location. Note that for some combinations of rotations and reflections, TA (S ) and TD (S ) may have substantial overlap. Prob 2.9.4 Find a four function IFS with multiply-connected attractor, different from that shown on the right side of Fig. 2.62. Prob 2.9.5 Find a four function IFS with a totally disconnected attractor, or argue there is none. Prob 2.9.6 Find a four function IFS with a multiply-connected attractor, or argue there is none. Prob 2.9.7 Find a four function IFS with a dendrite attractor, or argue there is none. Hint: the dendrite is last for a reason. 96 2.10 CHAPTER 2. ITERATED FUNCTION SYSTEMS Coloring IFS by addresses In Sect. 5.2 we show how to adjust the probabilities of the transformations to assign colors to the IFS attractor by the probabilities of each region. This was the first way colors were assigned to IFS images, but it requires some background in measure theory. We need measure theory to define Hausdorff dimension, so Ch 3 might be a natural setting to develop this colorin...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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