Phyllotaxis
the spirals are counted, not admired
Generator

lewis-joint

The dashed line is Lewis's law, (n−2)/4. The fitted slope here is 0.009 against his 0.25, and the side count accounts for 16% of the variation in area.
Cell area against side count, at 0% disorderThe dashed line is Lewis's law, (n−2)/4. The fitted slope here is 0.009 against his 0.25, and the side count accounts for 16% of the variation in area.00.500155.5066.507sides of the cellarea, as a multiple of the mean cell areaLewis607 interior cellsslope 0.009 against 0.25

Drawn at its defaults, in packing and tiling. It carries a slider over jitter, so the claim in its caption strip is restated at every stop rather than at one. 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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