My approach would be something like this, but with a very "poor" generator with the parameters a=81007, c=0 and m=2^17. This approximates a low discrepancy sequ

My approach would be something like this, but with a very "poor" generator with the parameters a=81007, c=0 and m=2^17. This approximates a low discrepancy sequence (additive recurrence with alpha=1/golden ratio). Then I would calculate x and y values using the hilbert curve and the calculated pseudorandom number as the index (more precisely two Hilbert curves next to each other, so it covers a 512x256 rectangle). On today's CPUs it can be calculated quite fast (shameless selfplug: https://github.com/leni536/fast_hilbert_curve https://github.com/leni536/fast_hilbert_curve). I suspect that the resulting pattern on the screen would be less random looking, but more uniform without any obvious pattern.