John Shier and Paul Bourke An Algorithm for Random Fractal Filling of Space Computer Graphics Forum 32
Computational experiments with a simple algorithm show that it is possible to fill any spatial region with a random fractalization Q1 of any shape, with a continuous range of pre-specified fractal dimensions D. The algorithm is presented here in 1, 2 or 3 physical dimensions. The size power-law exponent c or the fractal dimension D can be specified ab initio over a substantial range. The method creates an infinite set of shapes whose areas (lengths, volumes) obey a power law and sum to the area (length and volume) to be filled.
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