Here you are seeing part of a pattern I created with my computer.

Can you either reproduce it or describe the algorithm I used?


The image is derived from a

golden bee tiling

and appears to have been produced via the following algorithm:

1: Initialize a 1:sqrt(1/phi) rectangle by placing the largest possible bees so each leaves a smaller rectangular area in the corner to be filled. Make them all red, like so:
enter image description here
2: As long as there exists a bee larger than some minimal size, decompose that bee into two smaller bees in the usual way. Color the smaller of the two new bees the same color as the original bee, and the larger one closer to blue. (Image from loopy walt, which isn't actually the above algorithm, but he provided it in the comments and I don't have an image of my own to present)

  • $\begingroup$ Well done, though you missed the luvely little pun I hid in the puzzle (it relies on alternative terminology, so to be fair maybe you didn't really have a chance). To make this a 10/10 answer, do you think you could work that out, too? Btw., I do not fully understand your initialisation procedure, I just assume it's correct. $\endgroup$
    – loopy walt
    Sep 6 '21 at 2:50
  • $\begingroup$ Here is a picture of the first few iterations. Feel free to use it. $\endgroup$
    – loopy walt
    Sep 6 '21 at 2:56

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