Real quadratic Julia sets can have arbitrarily high complexity

Cristobal Rojas; Michael Yampolsky

Real quadratic Julia sets can have arbitrarily high complexity

Dynamical Systems 2020-03-23 v3 Computational Complexity

Authors: Cristobal Rojas , Michael Yampolsky

Abstract

We show that there exist real parameters $c$ for which the Julia set $J_c$ of the quadratic map $z^2+c$ has arbitrarily high computational complexity. More precisely, we show that for any given complexity threshold $T(n)$ , there exist a real parameter $c$ such that the computational complexity of computing $J_c$ with $n$ bits of precision is higher than $T(n)$ . This is the first known class of real parameters with a non poly-time computable Julia set.

Keywords

julia set

Cite

@article{arxiv.1904.06204,
  title  = {Real quadratic Julia sets can have arbitrarily high complexity},
  author = {Cristobal Rojas and Michael Yampolsky},
  journal= {arXiv preprint arXiv:1904.06204},
  year   = {2020}
}

Comments

9 pages, 1 figure. To be published in the journal Found. Comp. Math. (FoCM). arXiv admin note: text overlap with arXiv:1703.04660

Real quadratic Julia sets can have arbitrarily high complexity

Abstract

Keywords

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