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Ah, I did not realize plotting is by default done with floats. By setting:
f(x,y)=mod2((N+floor(y/4)) / 2^(4*floor(x)+mod4(y)))
g=fast_callable(f, vars=[x,y], domain=RealField(100))
and contour_plot'ing g instead, which forces the use of higher-precision arithmetic, I get what I want.
