A Fast Algorithm for Julia Sets of Hyperbolic Rational Functions

The algorithm given in this paper computes Julia sets locally in time O(k⋅M(k)) (where M(k) denotes the time needed to multiply two k-bit numbers). Roughly speaking, the local time complexity is the number of Turing machine steps to decide a set of disks of spherical diameter 2−k so that the union of these disks has Hausdorff distance at most 2−k+2. This allows to give reliable pictures of Julia sets to arbitrary precision.