It's super nit-picky of me to point out: the double and add visualization is a meme among professional elliptic curve guys.

You are in fact drawing a hyperbola between points on an (almost) circular plane. However, you won't find this published anywhere idk why. It's just one of those things you get from spending 3 years in office hours with the 73 year old math professor who's worked on elliptic curves since they became mainstream in the 1980's.

My PhD advisor demanded I use Julia for my dissertation. Back then I was a junior programmer so Julia's one-based indexing absolutely threw me off.

In retrospect, the PhD experience was miserable and using Julia contributed to my 'death by a thousand cuts'.