How about Hilbert's squarefill evaluated with a fixed, irrational step size?gosper.org/hilbrand.png --rwg --I like that. I had the idea (did I post it?) another time of integrating high-dimensional functions by regarding them as 1D integrals along a spacefilling curve... which hopefully would work better than plain monte-carlo integration. One could also "adapt" rather easily using that approach. Is the nearest-neighbor distance-distribution different for this kind of point set, than for random points? (I presume yes, but can see that arbitrarily small distances still do occur.) --wds If that's bad, you can choose a beating frequency close to a self-avoiding frequency: gosper.org/hilbeat.png Here (again) is the exact Hilbert fcn Clear[Hilbert]; Hilbert[t_, a1_: 1, a0_: 0] := Hilbert[t, b1_: 1, b0_: 0] = (Hilbert[t, s1_: 1, s0_: 0] = ((a0 - s0)/(s1 - a1)); Module[{t4 = 4*t, n}, n = Floor[t4]; t4 -= n; Switch[n, 0, I*(1 - Hilbert[1 - t4, -I*a1/2, a0 + a1*I/2])/2, 1, (I + Hilbert[t4, a1/2, a0 + a1*I/2])/2, 2, (1 + I + Hilbert[t4, a1/2, a0 + a1*(1 + I)/2])/2, 3, 1 + I*Hilbert[1 - t4, a1*I/2, a0 + a1]/2, 4, 1]]) which is way too slow. You probably want the finite state machine version using dyadic rational approximations. --rwg As expected, that hourlong PrimeQ of SylvesterSequence[19] came up False: In[25]:= Timing[PrimeQ[Nest[#^2 - # + 1 &, 2, 19]]] Out[25]= {2737.828416, False}