Animating shapes

The classification table does not prevent shapes from animating, for example a swaying tree is still a 'tree', but if they change sufficiently that they move into and between different classifications then we can classify them by the set of classes that they transition between. Usually they are neighbouring classes, and in the examples below the transitions are within a square sub-section of the table. I use n-form to mean that these objects transition within an nxn square from their location at the bottom left corner. As you can see, some changes are fast, and others are over complete life cycles. 

 2 form void-cluster
 A 2 form void-cluster is a life cycle of a cluster going from nothing to small and then large objects.
This example is the life cycle of mushrooms. Ignoring the underground we see many tiny mushrooms spring up, as they grow they compete so there will only end up being a few large mushrooms and there are always a large distribution of sizes.
2d example video: http://vimeo.com/19769856 
 2 form cluster-tree
 This is a cycle of a tree to individual objects, in this example of cactuses they grow from fallen buds and when grown to a large size they produce new buds which drop off. So there is a cluster of cactuses and buds, with many more buds than fully grown cactuses. Each cactus is a tree topology.
 2 form tree-sponge
 This example is a tree blowing in the wind. The large branches bang against each other slowly and infrequently, the many smaller twigs touch against each other frequently. So it is a cycle between a tree and a tree-sponge in this case.
This class also includes a cycle where the tree branches fuse together to form a sponge.
2D example video: http://vimeo.com/19879237  

 2 form sponge-shell
 This termite mound is an encasing around a set of tunnels and chambers. At various stages of its life the chambers are self-connected and exposed through holes in the mound (sponge) or just branching chambers (shell), but never (or rarely) are chambers just blocked off to leave air pockets. Big chambers are few and small ones many.
 2 form shell-foam
 This hornet's nest is made up of small individual chambers that connect to larger chambers. During its life the chambers are blocked up (where new hornets are growing) and then broken through when the hornets hatch. The larger entrances may also be closed and moved, though less frequently. Chambers don't connect to each other, just to the larger ones which eventually connect to the outside. So it covers the forms of shell and foam.
 2 form foam-solid
 The life cycle of thick boiling volcanic mud is that there are many gaseous bubbles that form from nothing and grow. Only a few bubbles grow really large before they have risen to the surface. So the mud itself (considered solid compared to say water) covers the phase foam (bubbles) and solid (no bubbles).
     
 3 form void-tree
 These baobub trees represent a life cycle that goes from nothing (an arbitrarily small seed) to full tree shapes, but do not intersect, the branches do not touch, so it does not extend to a sponge form. 
As with most clusters of plants there are many small saplings and relatively fewer full size trees.
 3 form cluster-sponge
 These mango trees have many branches which knock against each other in a wind, so they have a sponge component, and unlike the trees above they do not spring from nothing but from the significant sized mangos. So a mango orchard contains the phases cluster, tree and sponge.
 3 form tree-shell
 The evolution of a mountain range over its lifetime is a 3 form tree-shell. It is made up of a fractal distribution of dips plus a fractal distribution of hills. During its life dips can replace where hills were and visa versa. Small scale hills and dips vary frequently, large mountains and basins only change very slowly.
 3 form sponge-foam
 This bumble bee nest is made of many individual chambers and larger chambers which all connect to each other to form a foam. During its life the chambers get blocked up for hatching of new bees, and broken out again, and the nest shape itself can evolve and grow. So this nest covers the phases of sponge through to foam (airtight chambers). 
 3 form shell-solid   The life cycle of this thick volcanic mud is more extreme than the 2 form example. It is hot enough that the bubbles can connect up to each other forming a connection of holes on the rising bubbles that temporarily connect the gaps and so making the mud a shell. So the cycles covers the phases from shell, foam and solid.
     
 4 form void-sponge
 A thick forest like this takes on many forms, at its thickest it is a sponge of crossing and touching branches, but also the seeds which the trees grow from are small enough to be considered that they are born from nothing. So the forest covers the phase void through sponge. Small plants are many and large trees are few.

 4 form cluster-shell
 The daffodil life cycle may barely fit into this category. They grow from bulbs so there is no void phase, and their leaves and petals could be considered a very basic shell form, so they have cluster and shell phases. Would be nice to find a better example for this class.
 4 form tree-foam
 This coral is tree-like in form, the branches close together to create pockets where the eggs grow before being released. So the coral itself (excluding eggs) is variously foam, tree and sponge in its form over the breeding cycle. Large pockets are rare and take longer between opening and closing (longer to grow the egg). 
 4 form sponge-solid
 This thick mud is hotter than the 3 form example and is bubbling a high enough rate that bubbles not only connect to the ones above but connect to others around creating a sponge or network of gaps between the mud that is always changing. Large gapes are few and small gaps many. 
 The bubbles grow from nothing with many small bubbles and fewer large ones. So it covers the phases from sponge to solid.
     
 5 form void-shell
 The many corals (a cluster) here grow from essentially nothing into branched trees of which the smaller sub-branches fuse together to form sponge and eventually fuse enough to create many planes so creating shell structures. The colourful coral here are also tree-like forms of leafy membranes. As with most life the small are many and large corals relatively few. 
 5 form cluster-foam  The energy of this lava is so high that it is continually boiling and churning to produce foam, sponge, dendritic outbursts and separate pieces of lava. However this example is so energetic that there isn't a pure solid phase. Also pieces of lava do not appear from nothing or disappear so there is no void phase either.
 Small outbursts are frequent and larger ones less so.
 5 form tree-solid
 Rolling lava is an example of a 5 form tree-solid. The cool outer rock has deep cracks in it that expose the glowing lava underneath. Such cracks give a tree shape to the rock, however the hot lava is continually absorbing the outer rock and growing new cracks so the lava flow changes phase between tree and solid. 
 Large cool areas are few and get recycled slowly, small cool areas are many and get recycled often.
     
 6 form void-foam
 At the largest scales the universe is a foam structure. As it evolves new areas are generated as dust collapses to stars and dendrites of galaxies connect to form sponge, shell and eventually foam structures. On this scale there are no areas of dense solid. Probably on galactic time scales this is a churning, boiling and bubbling foam.
 
 6 form cluster-solid

 This represents the life cycle of a cliff undergoing periodic rock falls. As such it covers the phases from a full solid to a cracked solid (tree solid) to a cluster solid then breaking away to a cluster. But the rocks never come from or go to void so void is not included. 
 At any time there may be different parts at different phases of this cycle. And small cracks and falls are more frequent than large ones.
     
 7 form void-solid
 Of all the things I can think of, fire best describes a 7-form void-solid. This class covers shapes that can take on virtually any form over their life time. It is hard to find examples that can do this out of moving solid pieces but that isn't necessary. Pieces of flame can grow from nothing (void, cluster phases), there can be branching fingers of flame (tree phase), connecting flames, flame surfaces and flames that temporarily surround gaps of air (sponge, shell, foam phases) and the solid flame is a void-solid. 
2d example video: http://vimeo.com/36951444  

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