Phyllotaxis
the spirals are counted, not admired
Generator

two-laws

Lewis's law wants disorder: its slope is 0.231 on the random set and 0.009 on the golden head. Aboav's relation wants order: a = 1.18 on the head, 0.59 on the random set.
Two laws, two tilings, and they disagree about which tiling is tissueLewis's law wants disorder: its slope is 0.231 on the random set and 0.009 on the golden head. Aboav's relation wants order: a = 1.18 on the head, 0.59 on the random set.Lewis slope — golden head0.009the law says 0.25Lewis slope — random set0.231the law says 0.25Aboav a — golden head1.177the law says 1.2Aboav a — random set0.593the law says 1.2filled where the tiling obeys the law it is being judged by900 points in each tilingLewis explains 32% of the area spread at best

Drawn at its defaults, in packing and tiling. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 2 essays

the blast radius of changing it

Packing and tiling

Lewis's law wants disorder

Cell area rises linearly with side count — measured on cucumber epidermis in 1928 and quoted ever since as a property of packed tissue. It holds beautifully on a random point set, with a fitted constant of 1.64 against Lewis's 2. On a phyllotactic head it does not hold at all: the slope is 0.009, and area and side count are almost independent.

 Packing and tiling

Two laws that want opposite tissue

Lewis's law and Aboav's relation are quoted side by side as properties of cellular tissue. Measured on the same two tilings they point opposite ways — the ordered head satisfies Aboav's with the textbook value of 1.18 and fails Lewis's completely; the random set does exactly the reverse.

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