Phyllotaxis
the spirals are counted, not admired
Concept

Lewis's law — where it appears

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

Also named here as order and disorder — the same set of essays touches all of them, so they are one junction rather than several.

00.500155.5066.507sides of the cellarea, as a multiple of the mean cell areaLewis269 interior cellsslope 0.014 against 0.25

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.

tissue · lewis 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

Named alongside it

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

Order and disorderVoronoi cellsAboav–WeaireExplained varianceJoint distributionSummary statisticTopological correlation

All concepts