An Algorithm for Random Fractal Filling of Space. (29th July 2013)

• Record Type: Journal Article
• Authors: Shier, John; Bourke, Paul
• Is Part Of: Computer graphics forum. Volume 32:Number 8(2013)
• Page Start: 89
• Page End: 97
• Publication Date: 2013-07-29
• Subjects: Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.12163
• Languages: English
• ISSNs: 0167-7055

Abstract

<abstract abstract-type="graphical" xml:lang="en" id="cgf12163-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p>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"><graphic position="anchor" mimetype="image" xlink:href="ark:/27927/pgg3z3s1rzh" orientation="portrait" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /></boxed-text></p> </abstract>