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The Math Less Traveled 
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.
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