FractionalGeometry-Chap2

# While the cultural importance of these adventures is

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Unformatted text preview: 6, paint the region brown. Otherwise paint it green. the left image of Fig. 2.64 shows an example using ﬁve levels of iteration. We can add apples to the tree by painting a region red if, for example, the left-most address digist are 3, 3 (center tree in the ﬁgure) or 44 (right tree in the ﬁgure). More iterations and more intricate coloring instructions can produce quite a vatiety of trees, all from the same IFS rules. Figure 2.64: Left: an IFS tree with color assigned by addresses. Center and Right: apple trees This method of assigning colors is understandable, simple even, but not so elegant, paint-by-address replacing paint-by-number. At the very least, it gives more practice with addresses. Practice problems These problems use the IFS 1 2 3 4 r s θ ϕ 1/3 1/3 0 0 1/3 1/3 0 0 1/3 1/3 0 0 2/3 2/3 0 0 Table for the IFS of Prxs 2.10.1 e f 0 0 1/3 0 2/3 0 √ 1/6 3/6 and 2.10.2. Prxs 2.10.1 (a) Suppose we color the IFS attractor this way: green if the address contains 2 or 3, blue if it does not. Show the blue region is the line √ segment between (0, 0) and (1/2, 3). (b) What is the blue region of the attractor if those addresses containing 1 or 2 are painted green, those not containing 1 or 2 are painted blue? 98 CHAPTER 2. ITERATED FUNCTION SYSTEMS Prxs 2.10.2 The common address digit in...
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