Phyllotaxis
the spirals are counted, not admired
Concept

Search — where it appears

Looking for a case that may not exist, as against sweeping every point of a stated range. A search has to report where it looked as well as what it found, because a negative from one is worth only what its coverage is worth.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Twenty rises at the fine end of both branches, cut at every offset. One row per rise searched, coarse at the top of each block. The bar names the counted pair the stem shows and the numbers on the right are the lags its wrecking cuts leave standing. A pale row is a rise whose settled divergence has left the branch it was started from by more than 20 degrees, which is what happens below the ladder's finest rung — the pairs there are 2 and 4, 8 and 16, 11 and 22, which are not two consecutive terms of any additive sequence. One rise on the Lucas branch keeps a lag of 11 while still on it.

One rise below the census

Ten lattices were cut at every offset and their surviving lags came back as four numbers. One rise further down a rung the census already sweeps, three cuts keep a lag of eleven — which is a fifth number, on a lattice nothing about was unusual except that nobody had cut it.

cylinder · Ablation Twenty rises at the fine end of both branches, cut at every offset. One row per rise searched, coarse at the top of each block. The bar names the counted pair the stem shows and the numbers on the right are the lags its wrecking cuts leave standing. A pale row is a rise whose settled divergence has left the branch it was started from by more than 20 degrees, which is what happens below the ladder's finest rung — the pairs there are 2 and 4, 8 and 16, 11 and 22, which are not two consecutive terms of any additive sequence. One rise on the Lucas branch keeps a lag of 11 while still on it.

The lag that never survives

A correction to the exchange's size rests on four hop clusters, and a fifth would be the first real test of it. The prediction was written for a golden lattice at a lag of eleven. No golden lattice on this ladder reaches one, and the reason is a fact about the rule rather than about the search.

cylinder · Ablation The Lucas 7/11 rung between 0.007 and 0.006, cut at every rise. One row per offset, one column per rise of the search, coarse on the left. A pale cell is a rise at which that offset's cut recovers; a dark cell is a cut that wrecks and keeps a lag of 7; a warm cell is one that keeps 11. The nine intermediate rises of the ten-thousandth grid were cut first and the nine of the hundred-thousandth grid inside the one bracket they opened. The change sits between 0.0064 and 0.00639, one step of the grid the ladder names its rises on, and above it no cut keeps 11 anywhere.

One step of the grid, again

A search of the fine end stepped from one rise to another a hundred grid steps away, and the family a cut keeps changed somewhere between. Cutting the rises in between puts the change inside one step, with the lattice identical on both sides.

cylinder · Ablation

Named alongside it

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

AblationClaim testingContact familyHop lengthRungCensus designHonest limitsLattice offsetParastichy pairRiseDiscretisationIdentifiability

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