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- W64043368 abstract "This paper is concerned with a probabilistic algorithm for image generation. The simplest form of the algorithm is illustrated in Fig. 1. The leaf is generated as follows. Pick any point X 0 ∈ ℝ2. There are four affine transformations T : x → A x + b listed on top of this Fig., and four probabilities p i underneath them. Choose one of these transformations at random, according to the probabilities p i — say T k is chosen, and apply it to X 0, thereby obtaining X 1 = T k X 0. Then choose a transformation again at random, independent of the previous choice, and apply it to X 1, thereby obtaining X 2. Continue in this fashion, and plot the orbit {X n }. The result is the leaf shown. By tabulating the frequencies with which the points X n fall into the various pixels of the graphics window, one can actually plot the empirical distribution $${1 over {n + 1}}sumnolimits_{k = 0}^n {{delta _{{X_k}}}} $$ , using a grey scale to convert statistical frequency to color. The darker portions of the leaf correspond to high probability density." @default.
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- W64043368 date "1992-01-01" @default.
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- W64043368 title "Random Affine Iterated Function Systems: Mixing and Encoding" @default.
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- W64043368 doi "https://doi.org/10.1007/978-1-4612-0389-6_15" @default.
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