I concur that it is just a moiré pattern and issues from sampling. Once you 
get sufficiently far from the origin, the interval of r for frac(r^2) = 
(0,1) gets very small (in fact, very quickly). Contrast this with

f(x,y) = frac(sqrt(x^2+y^2))

It comes down to the sampling being done to make the 2d image.

Best,
Travis

On Thursday, February 27, 2025 at 1:14:34 AM UTC+9 Georgi Guninski wrote:

> 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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