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ISRN Computer Graphics
Volume 2012 (2012), Article ID 825782, 17 pages
http://dx.doi.org/10.5402/2012/825782
Research Article

GPU-Accelerated Rendering of Unbounded Nonlinear Iterated Function System Fixed Points

University of Alaska Fairbanks, Fairbanks, AK 99775, USA

Received 31 October 2011; Accepted 7 December 2011

Academic Editors: T. Calvert, M. Kraus, and L. Ma

Copyright © 2012 Orion Sky Lawlor. 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.

Abstract

Nonlinear functions, including nonlinear iterated function systems, have interesting fixed points. We present a non-Lipschitz theoretical approach to nonlinear function system fixed points which generalizes to noncontractive functions, compare several methods for evaluating such fixed points on modern graphics hardware, and present a nonlinear generalization of Barnsley’s Deterministic Iteration Algorithm. Unlike the many existing randomized rendering algorithms, this deterministic method avoids noncoherent branching and memory access and takes advantage of programmable texture mapping hardware. Together with the performance potential of modern graphics hardware, this allows us to animate high-quality and high-definition fixed points in real time.