Abstract

We show that there exist real parameters c∈ (- 2 , 0) for which the Julia set Jc of the quadratic map z2+ 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 Jc 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.