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Issue No.01 - January (1995 vol.15)
pp: 32-41
ABSTRACT
Heavy computation requirements have inhibited the application of fractal technology, but new algorithms for coding and displaying Iterated Function System fractals are achieving real-time performance.
INDEX TERMS
fractals, Iterated Function System fractals, fractal algorithms
CITATION
Donald M. Monro, Frank Dudbridge, "Rendering Algorithms for Deterministic Fractals", IEEE Computer Graphics and Applications, vol.15, no. 1, pp. 32-41, January 1995, doi:10.1109/38.364961
REFERENCES
1. M.F. Barnsley and S. Demko, “Iterated Function Systems and the Global Construction of Fractals,” Proc. Royal Soc. London, Vol. A399, 1985, pp. 243-275.
2. M.F. Barnsley, Fractals Everywhere, Academic Press, San Diego, Calif., 1988.
3. S. Dubuc and A. Elqortobi, “Approximations of Fractal Sets,” J. Computational and Applied Mathematics, Vol. 29, 1990, pp. 78-89.
4. D.M. Monro, F. Dudbridge, and A. Wilson, “Deterministic Rendering of Self Affine Fractals,” IEE Colloquium on Fractal Techniques in Image Processing, Digest No. 1990/171, IEE, Hitchin, Herts, UK, 1990, pp. 5/1-5/4.
5. J.E. Hutchinson, “Fractals and Self-Similarity,” Indiana Univ. J. Mathematics, Vol. 30, No. 5, 1981, pp. 713-747.
6. J. Elton, “An Ergodic Theorem for Iterated Maps,” J. Ergodic Theory and Dynamical Systems, Vol. 7, 1987, pp. 481-488.
7. S.G. Hoggar and L. Menzies, “Jigsaws and Faster Fractal Pictures,” to appear in Proc. IMAConf. Image Processing, Oxford Univ. Press, 1994.
8. M.F. Barnsley et al., “Solution of an Inverse Problem for Fractals and Other Sets,” Proc. Nat’l Academy of Sciences, Vol. 83, 1986, pp. 1,975-1,977.
9. S. Graf, “Barnsley’s Scheme for the Fractal Encoding of Images,” J. Complexity, Vol. 8, 1992, pp. 72-78.
10. M.F. Barnsley, “Fractal Functions and Interpolation,” Constructive Approximation, Vol. 2, 1986, pp. 303-329.
11. A.E. Jacquin, "Image Coding Based on a Fractal Theory of Iterated Contractive Image Transformations," IEEE Trans. Image Processing, Vol. 1, No. 1, Jan. 1992, pp. 18-30.
12. D.M. Monro, “A Hybrid Fractal Transform,” Proc. IEEE Conf. Acoustics, Speech and Signal Processing, IEEE Press, Piscataway, N.J., Vol. 5, 1993, pp. 169-172.
13. D.L. Wilson, J.A. Nicholls, and D.M. Monro, “Rate-Buffered Fractal Video,” Proc. IEEE Conf. Acoustics, Speech and Signal Processing, IEEE, Piscataway, N.J., Vol. 5, 1994, pp. 505-508.
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