An Algorithm for Random Fractal Filling of Space. (29th July 2013) - Shier, John; Bourke, Paul
<x xml:space="preserve">Abstract</x> 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. <boxed-text content-type="graphic" position="anchor" orientation="portrait"> </boxed-text>