FractionalGeometry-Chap2

In computational terms this means the nite sequence

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Unformatted text preview: generating the image. 2.4. CONVERGENCE OF RANDOM IFS 51 But rotation isn’t a contraction. Can IFS attractors be generated in some other way? With the question posed in that fashion, the answer must be yes. The random IFS algorithm is less demanding of computer memory and gives a more rapid sketch of the major features of the attractor. In addition, although we’ll develop the random IFS algorithm in the setting where all the transformations are contractions, Elton [48] has developed a beautiful extension of these ideas to show the random algorithm generates the attractor when the transformations are contractions on average. To understand a thrid reason for learning the random IFS algoithm, we need a brief description of how it works. More detail is given later in this section. The random IFS algorithm for the IFS {T1 , . . . , Tn }, with attractor A, works in this way. 1. Begin with the fixed point (x0 , y0 ) of one of the Ti . For formulas to locate the fixed point, see Exercise 2.4.1. 2. Giv...
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