Phyllotaxis
the spirals are counted, not admired
Series

Shape exponent — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. The exponent sets the spacing, and only the exponent. The curve is φ^(2/p), drawn from the ladder's ratio of 1/φ² and nothing else. The dots are measured: each surface built, a blind counter walked up its axis, the places its answer changed recorded. A cone that elongates and a paraboloid that fills sit on the same point at p = 1 — so the spacing identifies neither the shape nor the way material arrives, only their product.

    The shape and the law

    A cone's transitions are a factor of φ² apart and a disc's a factor of φ, and the temptation is to read the ratio as the shape. It is not. Five surfaces built and counted show that the ratio measures one exponent, and that the exponent is the shape multiplied by the way material arrives.

    part 4 · cylinder

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