An Algorithm for Random Fractal Filling of Space
Article first published online: 29 JUL 2013
© 2013 The Authors Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Computer Graphics Forum
Volume 32, Issue 8, pages 89–97, December 2013
How to Cite
Shier, J. and Bourke, P. (2013), An Algorithm for Random Fractal Filling of Space. Computer Graphics Forum, 32: 89–97. doi: 10.1111/cgf.12163
- Issue published online: 27 NOV 2013
- Article first published online: 29 JUL 2013
- space filling;
- G.3 [Mathematics of Computing]: Probability and Statistics–Stochastic processes;
- I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling–Geometric algorithms, languages, and systems;
- I.3.m [Computer Graphics]: Miscellaneous
Computational experiments with a simple algorithm show that it is possible to fill any spatial region with a random fractalization 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. The algorithm begins by randomly placing the largest shape and continues using random search to place each smaller shape where it does not overlap or touch any previously placed shape. The resulting gasket is a single connected object.