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On computational complexity of Siegel Julia sets

I. Binder·M. Braverman·M. Yampolsky
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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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I. Binder, M. Braverman, M. Yampolsky. 2005-11-07. On computational complexity of Siegel Julia sets. https://doi.org/10.1007/s00220-006-1546-3

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