Arguably Psychedelia by Jeff Minter [1] has a claim to be the first software music visualiser. The algorithm is pretty straightforward [2] and I recently 'ported' it to Javascript for fun.[3]

[1] https://en.wikipedia.org/wiki/Psychedelia_(light_synthesizer... [2] https://github.com/mwenge/psychedelia [3] https://mwenge.github.io/psychedelia.large/