Communications in Mathematical Physics

, Volume 291, Issue 2, pp 513–532 | Cite as

Constructing Locally Connected Non-Computable Julia Sets

  • Mark Braverman
  • Michael Yampolsky


A locally connected quadratic Siegel Julia set has a simple explicit topological model. Such a set is computable if there exists an algorithm to draw it on a computer screen with an arbitrary resolution. We constructively produce parameter values for Siegel quadratics for which the Julia sets are non-computable, yet locally connected.


Turing Machine Rotation Number Blaschke Product Continue Fraction Expansion Critical Orbit 
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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Microsoft Research New EnglandCambridgeUSA
  2. 2.Mathematics DepartmentUniversity of TorontoTorontoCanada

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