but conceals the local phyllotactic order of neighbor sites along the parastichies. In these sequences, we have bracketed the grain boundaries as $[...]$ and gathered sites in groups $[(f_{i-1}), (f_{i-2}), (f_{i-1})]$, unless it is obvious.

We now discuss a dramatic manifestation of the organization of phyllotaxis and of its malleability in the agave.

Anomalous growth: The agave
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An application of phyllotaxis to growth with the plasticity imparted by the grain boundaries can be seen in the natural history of Agave Parryi (Fig.\[f5\]). Structurally, it spends almost its entire life (24.5 years) as a conventional, spherical cactus in phyllotaxis $(13,8,5)$ which is also that of the pineapple. During the last six month of its life, it sprouts a huge mast terminating as seeds-loaded branches.

The agave is a spherical phyllotaxis $n = 43-75$, $(5,6,6),[(6,6,6,6,6),(6,6,6),(5,5,5,5,5)],6,6,..;\dots$, a single grain $(13,8,5)$ bounded by two grain boundaries (polar circles) $[(6,6,6,6,6),(6,6,6),(5,5,5,5,5)]$ and\
$[(5,5,5,5,5),(6,6,6),(6,6,6,6,6)]$ on which the cells are square and the vertices critical points for $T1$ (Fig.\[f6\]a). Growth proceeds from the bottom, from the south to the north pole of the sphere. The south polar cap consists of a first layer of three cells $(5,6,6)$ with the south polar circle.

How does growth proceed beyond 