I understand everything except the second image, I think.
The second image is built on exactly the same principle as all the others. I don’t know if the coloring scheme is throwing you off; don’t try to read too much into the colors, which I chose only to make things look nice.
I thought the same! There’s the sequence: 1×1+1,1×2+1,2×2+1,2×3+1,3×3+1. Which would mean 3 colors for the second image, in lines at 45 degrees. Would that one also fit your pattern?
Oh, I had miscounted the last image – I thought it was a cycle of 11 and the others were 2, ?, 5, 7.
There’s actually no particular pattern to the *sequence* of images; I just chose various ones that are all generated by the same scheme. But yes, 3 colors in lines at 45 degrees is one possible image that can be generated by this scheme.
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I understand all the images except the 4th as residue classes mod some Gaussian integer.
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