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<p>The presented algorithm generates approximations of self-similar fractal sets. The algorithm is based on a pattern rewriting system that draws a geometric pattern repeatedly after suitable mappings. A program developed from the algorithm reproduces Mandelbrot's self-similar fractals. We begin by discussing fractals and dimension theory, then present the algorithm, and conclude by using fractal set theory to calculate the dimensions of self-similar sets from their generators.</p>
Nicholas F. Reingold, Stephen D. Casey, "Self-Similar Fractal Sets: Theory and Procedure", IEEE Computer Graphics and Applications, vol. 14, no. , pp. 73-82, May/June 1994, doi:10.1109/38.279048
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