Let $f(x,y)$ be polynomial with integer coefficients.
Pick integer $n>2$.
Let $M$ be $n \times n$ matrix. Set $M_{i,j}=f(i,j) \mod n$.
Plot $M$ as bitmap in shadows of gray where larger value is lighter and smaller is darker. (Zero is black).
Experiments suggest the resulting plot in shadows of gray sometimes resembles the real locus of the affine curve $f(x,y)=0$.
Is this true?
If this is true how to explain it?
Actually such relation between discrete and continuous surprises dumb me.
Here are some plots for $n=213$ done in Sage.
$$x^2+y^2-1$$
$$x^2+2y^2-1$$
$$x^2-y^2-1$$
$$x^3-y^2-1$$ (might be counterexample)
$ x^2+y^2-1$, white is zero, black is nonzero.
$x^2+2y^2-1$ with colormap 'gnuplot', check sage's documentation.
