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In the movie, tumbling blue spheres are stacked on each other, with their centers on a virtual cylinder. Suddenly, a transparant hemisphere closes the cylinder, and the balls are forced to close the surface.
Now, the virtual glass bell shrinks and disappears. This marks the starting point of strong expansion of the structure. While the top expands radially, a regular flower pattern arises.

You will wonder why the spheres fall from heaven. This is done to accentuate that this is only a model for phyllotaxis, not a movie of a plant.