This is a picture of the integer points (x,y,z) with x

For every point (x,y,z), there is some N with x

The little black dots correspond to points where z=0, so N is the sum of two squares, which is possible depdning on the prime factors mod 4. https://en.wikipedia.org/wiki/Sum_of_two_squares_theorem.

You can choose to either scale the grid to fit the screen, or keep the same scale througout. You can change N by the slider, or have it automatically change for a pretty animation.

I put in an option to see the colours of (x,y) depdending on the largest i < N with some z with (x,y,z).(x,y,z)=i. OR, depending on smallest such i. This reminded me of this https://gallery.bridgesmathart.org/exhibitions/2022-bridges-conference-short-film-festival/henrys.