Hi Simon :)

google "plasma demo source" for 90% of the technical details. basically take a smooth function (typically trig, but linear/exp/dist/subdivision fractal/gaussian blurred photo, etc will all work), have several origins that move through it and add up the values from each origin (demo scene stuff will prebuild a big table, then just increment two or more indexes through it, read values, add 'em, set pixel - very fast, this ain't nearly that fast yet!)

that's basically what Perlin noise is, essentially, but Perlin formalized the "octaves" mechanism (higher frequencies added at lower amplitude) to get smaller details, in a manner basically like AM synthesis does for sound waves.

..anyway!..

so this is two such fields in 3.5D (xyz time animated), one controls theta (local y rotation) other controls phi (local x rotation), their sum controls local scaling, then the whole thing rotated slowly globally.

Yeah! Great!!!!
and thanks for the details :)