I have some function $z=f(x,y)$ with $x,y,z$ real numbers. I wrote a script that generates a $600\times 600$ pixels plot of this function for, say, $0 < x < 1$ and $0 < y<1$, by mapping z to some color gradients. Now, because $f(x,y)$ is somewhat convoluted, the plot contains some nice moiré patterns that I find esthetically pleasing. Therefore I'd like to make a bigger version of this plot, say $3000\times 3000$ pixels, still with $0 < x < 1$ and $0< y <1$. Unfortunately when I do this the obvious way (by just calculating more points), the moiré fringes become much narrower and the result is not as interesting as the original.
So my question: is there a way to generate the bigger plot and still keep the moiré patterns at the same size as the original plot?