Interesting. I have an OCD/tic that leads me to count digit sum sequences (less so now than earlier in life). Sometimes I'll count them in the base 10 system, other times I'll use the clock system (cycling over at the 60 marks). I've noticed patterns when doing this, but haven't yet iterated the entire system, and have only briefly iterated other base systems (the clock system is closed, so is fully iterable, and must return to its starting point, but even open-ended base 10 has noticeable patterns).

The digit summing is generally similar to Fibonacci summing (though I do it on the individual digits usually, not the full numbers, e.g. 8+13 = 12 instead of 21).

Any particular reason why the colors flipped for the 34x55 rectangle? Is this a different part of the pattern? I can see in the larger header that there are regions with single white squares (as seen in the 34x55 rectangle), just as there are regions with single purple square (as seen in the 8x13, 13x21, 21x34, and 55x89 examples).

This will be a long read that will take me a few days, so I'll leave this comment now.

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