Real quadratic Julia sets can have arbitrarily high complexity
share
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.
READ FULL TEXT