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I LOVE this idea! It reminds me of a project I did in high school, called a "Light Organ". You can really expand on this idea you already have by adding a simple bandpass circuit for each Red Green and Blue, for the Bass, Mid and Treble, adding a whole lot more variance to the patterns.
Well, as you describe a tree being fractal...the branches being a small scale of the tree...You do realize that the branches of any tree aren't truly like the whole tree, right? What you just described is exactly what is going on in these lichtenberg figures. Those branches burned in the wood look a lot like branches on a tree..."Lichtenberg figures are now known to be examples of fractals."https://en.wikipedia.org/wiki/Lichtenberg_figure
The Dream Machine or, How to Be More Awake While You Sleep
Is the best PCB etchant in every kitchen ?