Phyllotaxis
the spirals are counted, not admired
Concept

Aboav–Weaire — where it appears

2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
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

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.

tissue · cell laws 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

Named alongside it

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

Summary statisticVoronoi cellsCell areaDisorderEuler's formulaGolden angleLatticeLewis's lawMeasurementNull modelOrder and disorderPacking

All concepts