SRX Mathematics

SRX Mathematics / 2010 / Article

Research Article | Open Access

Volume 2010 |Article ID 432521 | 10 pages | https://doi.org/10.3814/2010/432521

Construction of Fractal Surfaces via Solutions of Partial Differential Equations

Received31 Jul 2009
Revised23 Sep 2009
Accepted13 Oct 2009
Published13 Jan 2010

Abstract

A new construction of fractal interpolation surfaces, using solutions of partial differential equations, is presented. We consider a set of interpolation points placed on a rectangular grid and a specific PDE, such that its Dirichlet's problem is uniquely solvable inside any given orthogonal region. We solve the PDE, using numerical methods, for a number of regions, to construct two functions H and B, which are then used to produce the fractal surface, as the attractor of an appropriately chosen recurrent iterated function system.

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Copyright © 2010 P. Bouboulis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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