Phyllotaxis
the spirals are counted, not admired
Concept

Topological defect — where it appears

A cell in a tessellated head that is not a hexagon, carrying a charge the hexagons around it do not. They are not scattered through the head: all 264 on a golden one sit within a cell's width of rings whose radii follow from the divergence angle alone.

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

135 fives and 129 sevens among 1631 interior cells. The side counts of every cell strictly inside a golden, 137.508° head of 2400 organs, cut at 86% of the radius. The fives and the sevens are counted apart rather than summed into a spread, because they are opposite charges and the sum hides them. Summed over the interior, 264 cells that are not hexagons carry a charge of +6. Over the whole patch the charge is 294, which is exactly 6 + 2·144 — a number fixed by the 144 cells on the patch's own boundary and carrying nothing whatever about the interior. The defects are not scarce; they are balanced.

An interior that is nearly neutral

Give every cell a charge of six minus its number of sides and the total over a tessellated head is fixed by its own boundary, exactly, with nothing left over for the interior. On a golden head that freedom is spent on 264 exceptions among 1,631 cells which cancel to six.

tissue · Topological charge 264 exceptions in a 2400-organ head, and eight circles. A golden, 137.508° head of 2400 organs, tessellated inside 86% of its radius. Every interior cell is drawn, and the 135 five-sided cells and 129 seven-sided ones are marked apart from the 1367 hexagons, and the pale circles are radii computed from the divergence angle through the lattice's third-shortest vector — nothing is fitted. Every defect sits within 0.64 of a cell spacing of one of those eight circles, and between them there is not one exception in hundreds of cells.

The defects lie on rings

The cells in a seed head that are not hexagons are not scattered through it. Every one of 264 sits within a cell of a radius computed from the divergence angle alone, the radii are a factor of φ apart, and between two of them lie 422 consecutive cells without a single exception.

tissue · Topological charge

Named alongside it

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

Topological chargeAnnulusCell spacingClaim testingDefect ringDelaunayDislocationEuler's formulaGeometric ladderHandoverHow many sidesLattice

All concepts