jugate-round-trip
Drawn at its defaults, in whorls, and patterns with k at a time. It takes no options at all, so every essay calling it gets this exact drawing.
Called by 5 essays
the blast radius of changing it
Two numbers out of the points
A seed head's divergence angle can be recovered from its spiral counts only to within an interval, because a range of angles gives the same counts. On a stem the counts come with lengths attached, two measurements pin two unknowns, and the lattice comes back to the last digit it was built with.
The claims, measuredWhat "whorled" was hiding
The expansion phase's census put 35% of divergences in a bucket labelled whorled and moved on. Opened, every pair in it is k and 2k — the coarsest rung of the ladder, repeated k times — and reading the census up to jugacy takes the Fibonacci share from 14.7% to 50.1% without describing a single extra plant.
The pattern itselfRecovering the angle from the counts
Build a head at a stated divergence angle, forget the angle, and get it back from the spiral counts alone. Four angles, worst error twelve thousandths of a degree — and the only thing that crossed between the two halves was a list of coordinates.
The pattern itselfTwo at a time
Every counter on this site asks how far it is from element i to element i plus m, and that index is a claim that the elements arrived one at a time. For teasel, for Cephalaria and for a real minority of plants the claim is false — and what those patterns turn out to be is an ordinary lattice, wrapped twice.
The pattern itselfCounting 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.