Phyllotaxis
the spirals are counted, not admired
Generator

response-on-both-branches

How far the next organ moves when the organ a given number of places back is removed, at a rise of 0.013, on a stem seeded onto the golden lattice and on one seeded onto the Lucas lattice. The shading is the size of the displacement and the vertical line is where the run of felt offsets ends: 8 on the golden stem, whose lattice is 5/8, and 7 on the Lucas stem, whose lattice is 4/7. Nothing else differs between the two runs. Everything that changes with the rise — the spacing, the heights, the size of the neighbourhood the rule sums over — is the same in both rows.
One rise, two seeds — the response of eachHow far the next organ moves when the organ a given number of places back is removed, at a rise of 0.013, on a stem seeded onto the golden lattice and on one seeded onto the Lucas lattice. The shading is the size of the displacement and the vertical line is where the run of felt offsets ends: 8 on the golden stem, whose lattice is 5/8, and 7 on the Lucas stem, whose lattice is 4/7. Nothing else differs between the two runs. Everything that changes with the rise — the spacing, the heights, the size of the neighbourhood the rule sums over — is the same in both rows.123456789101112golden5/8, front 81234567891011Lucas4/7, front 7organ removed, places back from the tiprise 0.015 · same rule, same grid, same heightsfronts 8 and 7

Drawn at its defaults, in two branches at one rise. It carries a slider over rise, so the claim in its caption strip is restated at every stop rather than at one. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 3 essays

the blast radius of changing it

Stems and cones

Seven rises and two seeds

One organ removed from a stem is felt out to the larger of its two spiral counts. Every test of that has confounded the count with the rise, because on one branch the two move together. Grow a second branch beside the first at the same rise and they come apart — and doing it at seven rises turns a matched pair into a design whose last column changes hands four times.

 Stems and cones

The front that reads one short

Eleven cells of a fourteen-cell design put the boundary exactly at the larger spiral count. Three put it one offset earlier, and the tempting move is to lower the threshold until all fourteen agree. Measured instead of tuned, the three turn out to be the three cells nearest below their own rung's boundary — and the last offset of a front is weak because it has only just arrived.

 Stems and cones

The hole on the other branch

Near a transition, the run of offsets a stem notices stops being a run: there is quiet past the front and then one isolated offset, felt as hard as anything inside it. Where that offset sits was pinned down on Fibonacci lattices, where the numbers to check it against are 5, 8 and 13. On the Lucas branch they are 4, 7 and 11 — and the rule holds there too.

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