Trying to figure out how to distinguish between numerators in angled internal addresses, from just the complex points C and its iterates Z (the marked points on the Hubbard trees). The angled internal addresses of the period 11 islands are 1 1/3 3 1/2 4 k/3 11 for k = 1, 2. If I can get an O(N) algorithm (here N is 11) to determine k from C then I will be very happy.

These images were made knowing the angles of the rays; finding the angles starting from C seems to be O(N^2) which is much too slow when N gets large.

I tried counting the number of clockwise-oriented triples of (period 4 iteration N, period 11 iteration N, period 11 iteration N + 4) for N in 1, 2, 3, and it allowed me to distinguish them.

But those filaments spiralled only a little, and the method fails with more curly locations like the one attached with angled internal address 1 2 3 1/8 23.

Colour is blue vs orange depending on the proportion of clockwise triples for (period 23 N, pixel N, pixel N+23) for N in 1,2...22.


I made a visualization of how the wakes spiral.

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