Thanks for the plots.
Are you sure that the example with implicit_plot and plot_points=800
doesn't have patterns?
I suspect that precision issues (float?) together with small "pixel"
size incorrectly kill the pattern.

implicit_plot(lambda u, v:frac(u^2+v^2)-0.5, (13, 14), (13, 14),
plot_points=800)
shows lines, not sure if this is correct.
I think if you increase the number of points you must zoom in,
decreasing the size of the region.

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