Phyllotaxis
the spirals are counted, not admired
Generator

branch-fronts

How many organs back a single removal is still felt, on a stem seeded onto the golden lattice and on one seeded onto the Lucas lattice, at seven rises. Everything but the seed is identical at each rise — the rule, the spacing, the heights, the azimuth grid — and the two fronts differ at every one of them. Which branch has the wider front changes hands four times going down the range, so no function of the rise gives the column. The golden branch carries 5/8 at four of these rises, across a factor of two in the rise, and its front is eight at all four.
The same rule, the same rise, two lattices, two frontsHow many organs back a single removal is still felt, on a stem seeded onto the golden lattice and on one seeded onto the Lucas lattice, at seven rises. Everything but the seed is identical at each rise — the rule, the spacing, the heights, the azimuth grid — and the two fronts differ at every one of them. Which branch has the wider front changes hands four times going down the range, so no function of the rise gives the column. The golden branch carries 5/8 at four of these rises, across a factor of two in the rise, and its front is eight at all four.456781011121.621.701.801.8922.102.22rise (falling to the right)how deep the front is, in organs3/53/44/75/87/118/13goldenLucas7 rises · both branches settled to under 0.5°4 reversals

Drawn at its defaults, in two branches at one rise. 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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