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fractals & statistical growth 345Figure 13.9 The rules for two versions of the Game of Life, given graphically on the top row,create the gaskets below. (Output of this sort is obtained from the applet JCellAut onthe CD.)In 1983 Wolfram developed the statistical mechanics of cellular automata andindicated how one can be used to generate a Sierpiński gasket [Wolf 83]. Since wehave already seen that a Sierpiński gasket exhibits fractal geometry (§13.2), thisrepresents a microscopic model of how fractals may occur in nature. This modeluses eight rules, given graphically at the top of Figure 13.9, to generate new cellsfrom old. We see all possible configurations for three cells in the top row, andthe begetted next generation in the row below. At the bottom of Figure 13.9 isa Sierpiński gasket of the type created by the applet JCellAut on the CD (underApplets). This plays the game and lets you watch and control the growth of thegasket.C D13.10 Perlin Noise Adds Realism ⊙We have already seen in this chapter how statistical fractals are able to generate objectswith a striking resemblance to those in nature. This appearance of realism may befurther enhanced by including a type of coherent randomness known as Perlin noise.The resulting textures so resemble those of clouds, smoke, and fire that one cannot helpbut wonder if a similar mechanism might also be occurring in nature. The techniquewe are about to discuss was developed by Ken Perlin of New York University, whowon an Academy Award (an Oscar) in 1997 for it and has continued to improve it[Perlin]. This type of coherent noise has found use in important physics simulationsof stochastic media [Tick 04], as well as in video games and motion pictures (Tron).−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 345