Abstract
In this paper, we introduce probabilistic affine automata (PAA) which are probabilistic finite generators having transitions labeled with affine transformations. It is shown that PAA are capable of generating highly complex images. Barnsley's IFS method to generate fractals is a special case of PAA when the automaton happens to have only a single state.
This research was supported by the National Sciences Foundation under Grant No. CCR-8702752.
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
M. F. Barnsley, Fractals Everywhere, Academic Press, 1988.
M. F. Barnsley, J. H. Elton and D. P. Hardin, “Recurrent Iterated Function Systems”, Constructive Approximation, 5 3–31 (1989).
M. F. Barnsley, A. Jacquin, L. Reuter and A. D. Sloan, “Harnessing Chaos for Image Synthesis”, Computer Graphics, SIGGARPH 1988 Conference Proceedings.
K. Culik and S. Dube, “Image Synthesis using Affine Automata”, Technical Report TR90004, Dept. of Computer Science, Univ. of S. Carolina.
K. Culik and S. Dube, “Image Synthesis using Rational Expressions”, Technical Report TR90001, Dept. of Computer Science, Univ. of S. Carolina.
D. B. Ellis and M. G. Branton, “Non-Self-Similar Attractors of Hyberbolic IFS”, in: J. C. Alexander (Ed.), Dynamical Systems, Lecture Notes in Mathematics 1342, pp. 158–171, Springer-Verlag, 1988.
J.Gleick, Chaos-Making a New Science, Penguin Books, 1988.
B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Co., San Francisco, 1982.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Culik, K., Dube, S. (1990). Affine automata: A technique to generate complex images. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029612
Download citation
DOI: https://doi.org/10.1007/BFb0029612
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52953-8
Online ISBN: 978-3-540-47185-1
eBook Packages: Springer Book Archive