ISRN Computer Graphics
Volume 2012 (2012), Article ID 825782, 17 pages
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.
- R. F. Williams, “Composition of contractions,” Boletim da Sociedade Brasileira de Matemática, vol. 2, no. 2, pp. 55–59, 1971.
- A. Tychonoff, “Ein fixpunktsatz,” Mathematische Annalen, vol. 111, no. 1, pp. 767–776, 1935.
- M. F. Barnsley, Fractals Everywhere, Morgan Kaufmann, 1993.
- S. Nikiel, Iterated Function Systems for Real-Time Image Synthesis, Springer, London, UK, 2007.
- S. Draves and E. Reckase, “The fractal flame algorithm,” 2003, http://flam3.com/flame.pdf.
- S. Draves, “The electric sheep screen-saver: a case study in aesthetic evolution,” in Applications of Evolutionary Computing, Proceedings of EvoMusArt05, 2005.
- S. Draves, “The electric sheep and their dreams in high fidelity,” in Proceedings of the 4th International Symposium on Non-Photorealistic Animation and Rendering (NPAR '06), pp. 7–9, June 2006.
- A. Lindenmayer, “Mathematical models for cellular interactions in development I. Filaments with one-sided inputs,” Journal of Theoretical Biology, vol. 18, no. 3, pp. 280–299, 1968.
- P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, Springer, New York, NY, USA, 1990.
- T. Ju, S. Schaefer, and R. Goldman, “Recursive turtle programs and iterated affine transformations,” Computers & Graphics, vol. 28, no. 6, pp. 991–1004, 2004.
- M. G. Peter Wonka, “Raytracing of nonlinear fractals,” in Proceedings of the 6th International Conference in Central Europe on Computer Graphics and Visualization (WSCG '98), pp. 424–431, Plzen, Czech Republic, February 1998.
- J. Hutchinson, “Fractals and self-similarity,” Indiana University Mathematics Journal, vol. 30, no. 5, pp. 713–747, 1981.
- J. J. van Wijk and D. Saupe, “Image based rendering of iterated function systems,” Computers & Graphics, vol. 28, no. 6, pp. 937–943, 2004.
- E. Gröller, “Modeling and rendering of nonlinear iterated function systems,” Computers & Graphics, vol. 18, no. 5, pp. 739–748, 1994.
- F. Raynal, E. Lutton, P. Collet, and M. Schoenauer, “Manipulation of non-linear IFS attractors using genetic programming,” in Proceedings of the Congress on Evolutionary Computation (CEC '99), pp. 1171–1177, IEEE Press, 1999.
- J. C. Hart and T. A. DeFanti, “Efficient anti-aliased rendering of 3D linear fractals,” in Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '91), vol. 25, pp. 91–100, 1991.
- J. Rice, “Spatial bounding of self-affine iterated function system attractor sets,” in Proceedings of the Graphics Interface Conference, pp. 107–115, May 1996.
- T. Martyn, “Tight bounding ball for affine IFS attractor,” Computers & Graphics, vol. 27, no. 4, pp. 535–552, 2003.
- O. S. Lawlor and J. Hart, “Bounding iterated function systems using convex optimization,” in Proceedings of the 11th Pacific Conference on Computer Graphics and Applications (PG '03), pp. 283–292, 2003.
- H. T. Chu and C. C. Chen, “On bounding boxes of iterated function system attractors,” Computers & Graphics, vol. 27, no. 3, pp. 407–414, 2003.
- O. S. Lawlor, Impostors for parallel interactive computer graphics, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2004.
- D. Saupe, “From classification to multi-dimensional keys,” in Fractal Image Compression—Theory and Applications to Digital Images, pp. 302–310, Springer, 1994.
- K. Datta, M. Murphy, V. Volkov et al., “Stencil computation optimization and auto-tuning on state-of-the-art multicore architectures,” in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC '08), pp. 1–12, IEEE Press, Piscataway, NJ, USA, 2008.
- D. M. Monro and F. Dudbridge, “Rendering algorithms for deterministic fractals,” IEEE Computer Graphics and Applications, vol. 15, no. 1, pp. 32–41, 1995.
- S. G. Green, “GPU-accelerated iterated function systems,” in Proceedings of the 32nd International Conference on Computer Graphics and Interactive Tichniques (SIGGRAPH '05 Sketches), p. 15, ACM, Los Angeles, Calif, USA, August 2005.
- S. Brodhead, “Flam4cuda: Gpu flame fractal renderer,” 2011, http://flam4.sourceforge.net/.
- D. M. Chandler and S. S. Hemami, “VSNR: a wavelet-based visual signal-to-noise ratio for natural images,” IEEE Transactions on Image Processing, vol. 16, no. 9, pp. 2284–2298, 2007.
- M. F. Barnsley, J. H. Elton, and D. P. Hardin, “Recurrent iterated function systems,” Constructive Approximation, vol. 5, no. 1, pp. 3–31, 1989.