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Affine automata: A technique to generate complex images

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Mathematical Foundations of Computer Science 1990 (MFCS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 452))

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.

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References

  1. M. F. Barnsley, Fractals Everywhere, Academic Press, 1988.

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  3. M. F. Barnsley, A. Jacquin, L. Reuter and A. D. Sloan, “Harnessing Chaos for Image Synthesis”, Computer Graphics, SIGGARPH 1988 Conference Proceedings.

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  4. K. Culik and S. Dube, “Image Synthesis using Affine Automata”, Technical Report TR90004, Dept. of Computer Science, Univ. of S. Carolina.

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  5. K. Culik and S. Dube, “Image Synthesis using Rational Expressions”, Technical Report TR90001, Dept. of Computer Science, Univ. of S. Carolina.

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  6. 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.

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  7. J.Gleick, Chaos-Making a New Science, Penguin Books, 1988.

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  8. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Co., San Francisco, 1982.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of South Carolina, 29208, Columbia, SC, USA

    Karel Culik II & Simant Dube

Authors
  1. Karel Culik II
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  2. Simant Dube
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Editor information

Branislav Rovan

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© 1990 Springer-Verlag Berlin Heidelberg

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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

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  • DOI: https://doi.org/10.1007/BFb0029612

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52953-8

  • Online ISBN: 978-3-540-47185-1

  • eBook Packages: Springer Book Archive

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