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Complexity of Julia Sets in Quadratics by Ianjamasimanana Roger is a document available to read on EtoBox.
Cristobal Rojas and Michael Yampolsky show that there exist real parameters c between -2 and 0 for which the Julia set of the quadratic map z^2 + c has arbitrarily high computational complexity. Specifically, for any threshold complexity function T(n), there is a real parameter c such that computing the Julia set with n bits of precision requires more than T(n) computational steps. This demonstrates the first known class of real parameters with a non-polynomial time computable Julia set.
- Author
- Ianjamasimanana Roger
- Language
- EN