\begin{align}

p_{n+1} = p_n + K \sin \theta_n, \\

\theta_{n+1} = \theta_n + p_{n+1},

\end{align}

with varying \(K\). It's pretty hypnotic https://www.shadertoy.com/view/WdjcW3

As it turns out, there is a better approach using Clenshaw's algorithm! A review of different methods is given in arXiv:1410.1748 [physics.chem-ph]. Now I could get up to high values of \(\ell\) and \(m\) without everything blowing up! From the ALPs we can then simply obtain the SHs as

\[

Y_\ell^m(\theta, \phi) = \sqrt{\frac{(2 \ell + 1) (\ell - m)!}{4\pi (\ell + m)!}} P_\ell^m (\cos \theta) e^{i m \phi}.

\]

The final code can be viewed at https://www.shadertoy.com/view/3dKGWG, which borrows from iq's shader

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Maybe I should do a small #introduction

Hello everyone! I'm Ron(i) and go by Roninkoi in most places. As a kid I started off making games for competitions such as #LDJAM, but these days I'm more into the technical side of things. Graphics programming and #creativecoding is my main interest, especially #demoscene and #retrocomputing. IRL I'm a computational #physics grad student working as a part-time code monkey

- Website
- https://www.roninkoi.net

- https://twitter.com/Roninkoi

- Github
- https://github.com/Roninkoi

I make games sometimes! Graphics programming enthusiast. Physics grad student. Finnish dragon ๐ฒ๐ซ๐ฎ๐

Joined Apr 2022