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Two related problems related to the complex quadratic polynomial $f_c(z) = z^2 + c$ and Mandlebrot and/or Julia sets:

  1. find an external angle $\theta_c$ for a complex point $c$

  2. find a complex point $c_\theta$ for an external angle $\theta$

Currently I can do both of these by tracing external rays (outwards for 1, inwards for 2), but it is asymptotically too slow to be practical: $O(n^2)$ where $n$ is the sum of the preperiod and period of the external angle.

Are there better algorithms? (What is the asymptotic cost of the Spider Algorithm, for example?)

Claude
  • 5,647
  • Maybe ask on the MathOverflow : Is it possibly to compute external angle with complexity < O(n^2) ? ( where n = ...) – Adam Dec 21 '17 at 18:39
  • cross-posted to: https://mathoverflow.net/questions/306866/fast-algorithms-for-external-angle-computations – Claude Jul 26 '18 at 02:09

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