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Few days ago I was recreating this (http://linas.org/art-gallery/self/wide.gif) in hopes to make an animation, but it turns out that changes get too subtle after 50th frame or so. Still, I think an interesting animation could be made if anyone finds a way to build interframes with unfolding branches for those 1st 50 frames (attached animation is fake made in winmorph just to give better idea of what I am talking about). The problem is, this is equivalent to finding smooth coordinates transform between two buds, which is a job for math genius like YOU :) so I am posting it here. In case anyone have an ideas...

Interesting animation. With a more basic approach I did this one a while ago:
http://www.youtube.com/watch?v=ULHZjnCp99c

exactly what I am talking about, ~20th second and onwards there is virtually no difference.

I think you might want your branch number growing faster - not linearly. Just take which ever parameter in the formula that represents the branch number, and replace it with exp(BranchNumber). You can also try cubic growth, or tangent growth - it would take you to infinite bulb number in finite time. Good luck, and let us see the anim once it's done!  :D

Yes I tried that (used fibonacci sequence) but this has a problem of max iterations needed to render this growing exponentially, and no significant diversity improvement within 1st 20 frames.

One interesting thing you could do is cycle between the different n-period buds. That is, the 1/23 bud, 2/23, 3/23, 4/23, 5/23, 6/23... 12/23. It might actually be more diverse than changing the denominator.

This way they should not branch, just wind into spiral, not sure if that also converges to identical image... But I have no general-case formula to try it out - help?