I’ve tried to draw the graphs of a function x ↦ x² in ℤ/pℤ for some of prime p’s. And the result gives me the feeling like I’m a medieval sage and I’m studying some sort of alchemy :)
Apparently we can see quadratic residues (the numbers which have at least one incoming arrow) and quadratic non-residues (have no incoming arrow). It is a visual representation of a fact that for each prime p there are equal amounts of both, which is (p-1)/2. Also, I could see two structures: cycles and trees, which are always combined and which I am curious to investigate further. Also it’s interesting how the number of connected components is related to the number p
It really feels like I gradually unveil the secrets of the universe. The look of my printed paper also gives an impression of an ancient scroll
