Pinqookie - Pinqookie

a girl

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

capricorn

People keep asking about this from time to time, so here is this little tutorial. I explained the best I could :,) Keep in mind this is just one way of doing it, and maybe you can change some of the steps to find one that works better for you. Hope it’s useful to someone out there!