Michael F. Barnsley
Abstract
Chaotic dynamics can be used to model shapes and render textures in digital images. This paper addresses the problem of how to model geometrically shapes and textures of two dimensional images using iterated function systems. The successful solution to this problem is demonstrated by the production and processing of synthetic images encoded from color photographs. The solution is achieved using two algorithms: (1) an interactive geometric modeling algorithm for finding iterated function system codes; and (2) a random iteration algorithm for computing the geometry and texture of images defined by iterated function system codes. Also, the underlying mathematical framework, where these two algorithms have their roots, is outlined. The algorithms are illustrated by showing how they can be used to produce images of clouds, mist and surf, seascapes and landscapes and even faces, all modeled from original photographs. The reasons for developing iterated function systems algorithms include their ability to produce complicated images and textures from small databases, and their potential for highly parallel implementation.
- Ambu 86 Amburn, P., Grant, E., Whitted, T., "Managing Geometric Complexity with Enhanced Procedural Methods," Computer Graphics, 20 (4) (August 1986). Google Scholar
Digital Library
- Barn 85a Barnsley, M. F. and Demko, S., "Iterated Function Systems and the Global Construction of Fractals," The Proceedings of the Royal Society of London A 399, pp. 243-275 (1985).Google ScholarCross Ref
- Barn 85b Barnsley, M. F., Ervin, V., Hardin, D. and Lancaster, J., "Solution of an Inverse Problem for Fractals and Other Sets," Proceedings of the National Academy of Science, Vol. 83 (April 1985).Google Scholar
- Barn 86a Barnsley, M. F., "Fractal Functions and Interpolation," Constructive Approximation, 2, pp. 303-329 (1986).Google ScholarCross Ref
- Barn 86b Barnsley, M. F., Elton, J., "A New Class of Markov Processes for Image Encoding, " to appear in the Journal of Applied Probability (1986).Google Scholar
- Barn 87 Barnsley, M. F., (SIGGRAPH tutorial) "Fractal Modelling of Real World Images," to appear in The Science of Fractals, Springer-Verlag, Berlin (1988). Google ScholarDigital Library
- Barn 88 Barnsley, M. F., Fraetals Everywhere, to appear, Academic Press (1988). Google ScholarDigital Library
- Bedf 86 Bedford, T. J., "Dimension and Dynamics for Fractal Recurrent Sets," Journal of the London Mathematical Society 2 (33), pp. 89-100 (1986).Google ScholarCross Ref
- Demk 85 Demko, S., Hodges, L., and Naylor, B., "Construction of Fractal Objects with Iterated Function Systems," Computer Graphics 19 (3), pp. 271-278 (July 1985). SIGGRAPH '85 Proceedings. Google ScholarDigital Library
- Diac 86 Diaconis, P., Shahshahani, M., "Products of Random Matrices and Computer Image Generation," Contemporary Mathamatics, 50, pp. 173-182 (1986).Google ScholarCross Ref
- Elto 86 Elton, J., "An Ergodic Theorem for Iterated Maps," To appear in the Journal of Ergodic Theory and Dynamical Systems (1986).Google Scholar
- Four 82 Fournier, A., Fussell, D., Carpenter, L., "Computer Rendering of Stochastic Models," Communications of the ACM 25 (6) (June 1982). Google ScholarDigital Library
- Hata 85 Hata, M. "On the Structure of Self-Similar Sets," Japan Journal of Applied Mathematics, 2 (2), pp. 381-414 (Dec. 1985).Google ScholarCross Ref
- Hutc 81 Hutchinson, J., "Fractals and Self-similarity," Indiana University Journal of Mathematics, 30, pp. 713-747 (1981).Google ScholarCross Ref
- Kawa 82 Kawaguchi, Y., "A Morphological Study of the Form of Nature," Computer Graphics, 16 (3), (July 1982). SIGGRAPH '82 Proceedings. Google ScholarDigital Library
- Mand 82 Mandelbrot, B., The Practal Geometry of Nature, W. H. Freeman and Co., San Francisco (1982).Google Scholar
- Mill 86 Miller, G. S. P., "The Definition and Rendering of Terrain Maps," Computer Graphics, 20 (4), (August 1986). SIGGRAPH '86 Proceedings. Google ScholarDigital Library
- Oppe 86 Oppenheimer, P. E., "Real Time Design and Animation of Fractal Plants and Trees," Computer Graphics, 20 (4), (August 1986). Google ScholarDigital Library
- Reut 87 Reuter, L., "Rendering and Magnification of Fractals using Iterated Function Systems", Ph.D. Thesis, Georgia Institute of Technology, Dec 1987. Google ScholarDigital Library
- Smit 84 Smith, A. R., "Plants, Fractals, and Formal Languages," Computer Graphics 18 (3), pp. 1-10 (July 1984). SIGGRAPH '84 Proceedings. Google ScholarDigital Library
Index Terms
- Harnessing chaos for image synthesis
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