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Polygon-Based Fractals from Compressed Iterated Function Systems
March/April 2010 (vol. 30 no. 2)
pp. 34-44
Philip Van Loocke, University of Ghent
A proposed method generates various fractal textures for regular polygons and allows the creation of polygon-based fractal flakes, polygon-based spirals, and many other forms. To control attractors in an understandable way, this method uses a small number of parameters. It's based on iterated function systems (IFSs) with linear holomorphic functions in one complex variable. To compress such systems, this method employs a contraction-free function. It also implements sth-order restriction, a new version of recurrent IFSs. Level-specified symmetry in the fractals is controlled through rth-level symmetrization.

1. M. Barnsley and S. Demko, "Iterated Function Systems and the Global Construction of Fractals," Proc. Royal Soc. London Series A, vol. 399, no. 1817, 1985, pp. 243–275.
2. M. Barnsley, Fractals Everywhere, Academic Press, 1988.
3. H. Peitgen, H. Jurgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer, 1992.
4. P. Prusinkiewicz and M. Hammel, "Language-Restricted Iterated Function Systems, Koch Constructions, and L-Systems," New Directions for Fractal Modeling in Computer Graphics, Siggraph '94 Course Notes, ACM Press, 1994, pp. 4-1–4-14.
5. M. Field and M. Golubitsky, Symmetry in Chaos: A Search for Pattern in Mathematics, Art, and Nature, Oxford Univ. Press, 1992.
6. S.-M. Ngai et al., "On 2-Reptiles in the Plane," Geometriae Dedicata, vol. 82, nos. 1–3, 2000, pp. 325–344.
7. S. Draves and E. Reckase, The Fractal Flame Algorithm, 2008; http://flam3.comflame_draves.pdf.
8. J. Van Wijk and D. Saupe, "Image Based Rendering of Iterated Function Systems," Computers & Graphics, vol. 28, no. 6, 2004, pp. 937–943.
9. D. Mumford, C. Series, and D. Wright, Indra's Pearls: The Vision of Felix Klein, Cambridge Univ. Press, 2002.
10. K. Jones and C. Reiter, "Chaotic Attractors with Cyclic Symmetry Revisited," Computers & Graphics, vol. 24, no. 2, 2000, pp. 271–282.
11. P. Van Loocke, "Non-linear Iterated Function Systems and the Creation of Regular Patterns over Regular Polygons," Computers & Graphics, vol. 33, no. 6, 2009, pp. 689–704
12. P. Van Loocke, "The Art of Iterated Function Systems with Expanding Functions," Proc. 2009 Bridges Banff Conf., Tarquin Books, 2009, pp. 55–62.

Index Terms:
iterated function systems, polygon, fractal texture, sth-order restriction, rth-level symmetry, computer graphics, graphics and multimedia
Citation:
Philip Van Loocke, "Polygon-Based Fractals from Compressed Iterated Function Systems," IEEE Computer Graphics and Applications, vol. 30, no. 2, pp. 34-44, March-April 2010, doi:10.1109/MCG.2009.84
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