Computational Intractability of Julia sets for real quadratic polynomials

04/11/2019

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by   Cristobal Rojas, et al.

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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.