Communications in Mathematical Physics

, Volume 264, Issue 2, pp 317–334 | Cite as

On Computational Complexity of Siegel Julia Sets

  • I. Binder
  • M. Braverman
  • M. Yampolsky


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.


Neural Network Statistical Physic Complex System Computational Complexity Nonlinear Dynamics 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • I. Binder
    • 1
  • M. Braverman
    • 1
  • M. Yampolsky
    • 1
  1. 1.Departments of Mathematics and Computer ScienceUniversity of TorontoTorontoCanada

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