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### Meta

Is this Euclid’s Orchard?

The coloring is the number of steps it takes the compute gcd(x,y) with the Euclidean algorithm.

Well done! I didn’t know whether anyone would figure out the coloring scheme.

It is! I wasn’t aware of that name for it, but I like it.

Is it about how many common divisors two Integers have?

You’re on the right track, but that’s not quite it.