PhaseLab
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As shown in this simplification of a cross section of a green stem, phyllotactic patterns arise just below the extreme apical tip. They are formed on the surface. Unlike the cell layers in lower regions, this skin is flexible.

Phyllotaxis is established in an early developmental stage. The physical laws in the plant top differ from those in our experience, and are beyond our intuition. It is not exactly right to characterize the changings in a plant top in terms of fluid motion. And it is a pity that we cannot trust our imagination of the qualities of buckling in a sheet of dough.