Phyllotaxis
the spirals are counted, not admired
Concept

Rim effect — where it appears

The distortion in any tessellation statistic caused by cells at the boundary, whose neighbours are missing rather than few.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

mean sides per cell(forced to six)mean squared departure from six(not forced)whorled, 144°5.9860.023golden, 137.508°5.9900.253rational, 137.5°5.9900.255Lucas, 99.502°6.0360.255137.0°5.9900.291Poisson5.9691.830six433–637 interior cells each, inside 86% of the radiussame cells, same cut, two statistics

The second moment is the measurement

The mean number of sides in a cellular tissue is six, and Euler's formula leaves it no choice — so it takes the same value on a golden-angle head, a whorled head and a set of random points. The mean squared departure from six varies by a factor of eighty across the same three, and almost nobody reports it.

tissue · sixsides a window on the head, 60% of its widthshare of all cell contactsby difference in placement index3431%5527%2117%8915%136%82%counted:34 and 55665 nodes · 1903 contacts · 5.72 per nodecoordinates in placement order, nothing else

The six are the spirals

Label every contact between two cells in a seed head with the difference between the two nodes' placement indices. The labels are the parastichy numbers — 34, 55, 21, 89 — and the six sides Euler forces turn out to be about two from one family, one and a half from the next, and one each from two more.

tissue · contact network

Named alongside it

The objects these essays reach for when they reach for this one.

Cell areaDisorderEuler's formulaGolden angleLatticeMeasurementPackingRational angleVoronoi cellsWhorledAboav–WeaireDelaunay

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