Construction of Fractal Surfaces via Solutions of Partial Differential Equations

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

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.