The plots show the number of solutions of an instance of the discrete logarithm problem finding k:
286\^k mod 289 = y
where y = mapping(x,y) for each pixel (x,y).
The first plot uses mapping(x,y) = x xor y, and the the second plot uses mapping(x,y) = x and y.
Edit: I had flaw in the code allowing solutions in 0 ≤ k < 289, which sometimes found two similar solutions for the discrete logarithm problem, eventhough it should only allow solutions in 0 ≤ k < totient(289) = 272. With this smaller search space the plot only shows two colors. The pattern stays the same though and is equal to checking whether mapping(x,y) ∈ Z*_289