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On Computational Complexity of Siegel Julia Sets

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Abstract

It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.

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Authors and Affiliations

  1. Departments of Mathematics and Computer Science, University of Toronto, Toronto, Ontario, M5S 2E4, Canada

    I. Binder, M. Braverman & M. Yampolsky

Authors
  1. I. Binder
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  2. M. Braverman
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  3. M. Yampolsky
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Additional information

Communicated by G. Gallavotti

The first and third authors are partially supported by NSERC Discovery grants. The second author is partially supported by NSERC Postgraduate Scholarship

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Binder, I., Braverman, M. & Yampolsky, M. On Computational Complexity of Siegel Julia Sets. Commun. Math. Phys. 264, 317–334 (2006). https://doi.org/10.1007/s00220-006-1546-3

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  • DOI: https://doi.org/10.1007/s00220-006-1546-3

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