An Algorithm for Random Fractal Filling of Space

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 exponen...

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Bibliographic Details
Published in:Computer graphics forum Vol. 32; no. 8; pp. 89 - 97
Main Authors: Shier, John, Bourke, Paul
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.12.2013
Subjects:
Algorithms
Analysis
and systems
Computer graphics
dimension
fractal
Fractals
G.3 [Mathematics of Computing]: Probability and Statistics-Stochastic processes
geometry
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling–Geometric algorithms, languages, and systems
I.3.m [Computer Graphics]: Miscellaneous
languages
packing
space filling
Studies
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary: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. 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.
Bibliography:istex:360EE11EDCC1E13C6D39F9D622E56A7A0D68BB87
ark:/67375/WNG-5F9J1RQ9-1
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ArticleID:CGF12163
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12163