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Or perhaps we could refer to his info page http://www.imagesavant.com/info.html

They're IFS fractals, I recommend either Apophysis 7x or Chaotica for creating them.

Doc Bailey had custom software. I had the pleasure of working with it on a bunch of films in combination with some rendering software I wrote.

Doc Bailey passed away quite some time ago now though and he never released the source code to my knowledge: https://vvvv.org/blog/richard-doc-bailey-(spore)-passed-away