On computational complexity of Siegel Julia sets

Details On computational complexity of Siegel Julia sets On computational complexity of Siegel Julia sets

2005-02-16

arxiv.org/abs/math/0502354v2

Mathematics

Dynamical Systems

Updated version, to appear in Commun. Math. Phys

Scientific paper

10.1007/s00220-006-1546-3

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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