Oh ok... well maybe you're right, I can't speak for hobold, but this is what I think:

- You can view an animating fractal by stacking each frame along a space dimensionAgree, yes it can be a helpful way to think about the animation

- The most interesting animating 2d fractals are the ones that when stacked are isotropic 3d fractalsDisagree. By the way, the growing circles fractal is not isotropic when stacked... the circles would need to grow then shrink.. and if you wanted growing squares or growing mushrooms it wouldn't be isotropic.

Back to the question.. how many forms can a dynamic fractal have?

There are 7 main classes of 3d fractal (void, cluster, tree, sponge, shell, foam, solid), but overall there is a 7x7 triangular table (

http://sites.google.com/site/mandelbox/what-class-of-fractal), which means 28 forms. This means a total of 2

^{28} different classes of dynamic fractal (

http://en.wikipedia.org/wiki/Combination#Number_of_k-combinations_for_all_k), which is 268 million classes... which doesn't make for a very good classification.

So instead we can classify these dynamic fractals by which triangular sub-table they range within. For example the 'void cluster + void sponge' dynamic fractal in the previous video ranges from void cluster up to void sponge, so includes dynamic fractals that also show a void tree form... this is natural because generally dynamic fractals that cover this range will show tree forms when going from a cluster to a sponge. The video is just a special case.

So in this classification, the most number of different forms a 3d dynamic fractal can change between is still 28, which is 7 main forms, and is called a 7-form void solid (it covers the full range from void to solid). The total number of different classes of dynamic fractal is then just 84, forming a 7x7x7 pyramid table.

What would such a maximum variation dynamic fractal look like? I'm not sure... it would obviously be massively shape shifting. The closest I could come up with is this boiling mud theme in 2d, after all boiling is a process of going from solid/liquid to gas (which is almost void). Most of the variation happens close to the surface: