inQ = Abs[FractionalPart[N[#, 16]]] < 0.1 &;
check[0 | 0., 0 | 0.] := 0;
check[a_, b_] :=
With[{p = (a + b)/(a^2 + b^2), q = (a - b)/(a^2 + b^2)},
Sum[Boole[inQ[c p] && inQ[c q]], {c, 100}]];
Monitor[
img = Table[(0.01 #)^(1/4) &@check[a, b], {a, -1, 1, 0.0025}, {b, -1,
1, 0.0025}];,
a]