Computability of Julia sets

2006/10/10 by Mark Braverman, Braverman, Mark, Michael Yampolsky +1 · 4 citations
Computer Science · Mathematics · #37F50 #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0610340

openalex publication_date 2006/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present an algorithm for constructing quadratics whose Julia sets are uncomputable. We also show that a filled Julia set of a polynomial is always computable.

Cited by

• Computable thermodynamic formalism
• A dynamical algorithm to compute hyperbolic Julia sets in polynomial time
• Computability for Axiom A Polynomial Skew Products of ℂ²
• Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space

Related

• Non-computable Julia sets
• Filled Julia sets with empty interior are computable
• On computability of Julia sets: answers to questions of Milnor and Shub
• Computability of the Julia set. Nonrecurrent critical orbits
• Real quadratic Julia sets can have arbitrarily high complexity