This image shows the "main" moire pattern (circles) in red, and the "contra-moire":

(y^2 + (d-x)^2)*(y^2 + (d+x)^2) = c

with green for c>d^4, and blue for c<d^4.

This is the moire formed by the "dual" to arithmetically increasing circles; the equations are:

x^2*(1 - (a^2/n^2)) + y^2 = n^2 - a^2.

For 0<n<a, this forms hyperbolas; for a<n, this forms ellipses. (Here a= 8). These two form a moire pattern which is the arithmetically increasing circles centered at x = +/- a. (A little squinting may be required here to see the circles!)