Phyllotaxis
the spirals are counted, not admired
Concept

Chain counting — where it appears

Counting a parastichy family by tracing each short lattice vector from point to point and counting the chains, which needs no order of arrival.

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

4 chains · counted pair 4 and 62-jugate at 69.35° · rise 0.064 chains in this family

Counting without an index

A person counting spirals on a cone puts a finger on one scale, follows a family round, and counts how many distinct chains there are. That needs no order of arrival — and building it turns out to be strictly more general than the counter the site had, and to find a bug in the counting of a bijugate stem that no assertion would have caught.

lattices · chain counting 0°45°90°135°180°front 1012345678910111213organ removed, places back from the tipas it comes outmodulo 180°2 organs a whorl · rise 0.0065 · counted 6/10 · symmetry 2generated from a stated rule, not drawn to look right

What a cut costs a whorl

A bijugate pattern is an ordinary lattice seen twice over, so the account that says a wrecked stem's repeating block is the repeat unit of the lattice underneath has a specific prediction here: three and five. It gets six and ten. And the thing a single missing organ does destroy on a whorled stem is the one property its counts cannot see.

cylinder · jugacy

Named alongside it

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

Counting blindJugacyRotational symmetryWhorlAblationAttractorBijugateCylinderHonest limitsLatticeLattice vectorsMeasurement

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