The column and row numbers figure in a pair of formulas, which then are tested for a greatest common divisor, GCD, of one (coprimes) or other small integers. The background is assigned a color. If the GCD is one, two, three, and so on, the cell is assigned black, blue, red, or yellow. For each plot there are two formulas, with the formula variables being row number and column number. For each cell, the two formulas are calculated, then the GCD of the numerical results are tested. The cell color is set accordingly. If the GCD is something other than one of the tested integers the cell remains the background color.
The GCD 3 digital drawings extend the process to the GCD of three numbers. The GCD of three numbers can be computed as gcd(a, b, c) = gcd(gcd(a, b), c). The third number can be used to mask or recompute areas selectively.
I don't design these patterns. I test formulas, and select colors to assign to the results. Other than that, the patterns come from the nature of the math. For example, the process for ten of the first plots is as follows.
a = row number
b = column number
If b>a then a and b are swapped. Each cell is assigned a color based on the greatest common divisor of the results of pairs of formulas such as:
1. a, b
2. a3+b3, a3–b3 (Taxicab and cabtaxi candidates)
3. b2+b+1, a2+a+1
4. b+a, b–a
5. b2+b+2, a2+a+2
6. b2–b+2, a2-a+1
7. b2+1, a2+2
8. b2+2b*a+a2, b2–2b*a–a2
9. b3+b2+b, a2+a
10. 3b3+2b2+b, 2a2+a
