That's an interesting concept. I think similar spigot algorithms are known for other transcendentals, and I suspect if you compared them you would not find a general trend of deep connections between algorithmic complexity and the geometric features of the corresponding value. What would you look for in the spigot algorithm for e, or log 2?
I suppose e's connection to hyperbolic geometry might suggest a relationship with the implicit formula x^2 - y^2 = 1. And I guess log2's behavior would be very much connected to that since it only differs from the natural log by a constant factor.
> "Partly because, mathematically, wavefunctions are vectors in a L^2 Hilbert space, which is complex-valued. Squaring the amplitude, rather Ψ∗Ψ=|Ψ|^2 is one way to ensure that you get real-valued probabilities, which is also related to the fact that […]"https://physics.stackexchange.com/questions/280748/why-do-we...
