I should have a rough draft pdf up soon, I'm currently making some graphs. The code is super slow, and still glitchy as fuck. I have to change some protocols from what they currently are. I'm doing recursion within recursion while we iterate a recursion within a recursion. Ffs, this is becoming nonsensical. But it's a better way than using Newton's root finder, which was the alternative way, lol.
This program is the slowest god damned thing. But here is a graph of \(\varphi\) done over \(90 \le y \le 100\) and \(0 \le s \le 0.2\) while \(x=3\). The foreground is as we increase\(s\). The lateral motion is increasing \(y\), where you see the stranger growth. The function looks a tad angular, numbers work out though. And it is analytic at these small angular jumps you see.
This is the exact value of \(\varphi\).
This program is the slowest god damned thing. But here is a graph of \(\varphi\) done over \(90 \le y \le 100\) and \(0 \le s \le 0.2\) while \(x=3\). The foreground is as we increase\(s\). The lateral motion is increasing \(y\), where you see the stranger growth. The function looks a tad angular, numbers work out though. And it is analytic at these small angular jumps you see.
This is the exact value of \(\varphi\).