julien-c

Relevant video: https://www.youtube.com/watch?v=5v5eBf2KwF8

I also tested in base 10, with primes under 1e9, got this:

             1       3       7       9
  1       0.0458  0.0746  0.0756  0.0540
  3       0.0599  0.0439  0.0707  0.0755
  7       0.0638  0.0677  0.0438  0.0747
  9       0.0805  0.0638  0.0599  0.0458

It appears to have the same transition probabilities as in base 5 (with the two center rows and columns swapped):

             1       2       3       4
  1       0.0458  0.0756  0.0746  0.0540
  2       0.0638  0.0438  0.0677  0.0747
  3       0.0599  0.0707  0.0439  0.0755
  4       0.0805  0.0599  0.0638  0.0458

I share your feeling about it being either obvious or deep.

It looks symmetric along the anti-diagonal. Strange.

Cool visualizations, nicely done. By the way there is a typo in the "Constraint Solving" section, in the last equation, it currently is

  c_x - b_y = 1

It should read

  c_x - b_x = 1