Phyllotaxis
the spirals are counted, not admired
Concept

Ensemble — where it appears

3 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
placement noisedegrees off the minimum00.250.50.7511.251.52field noisefraction of the barrier00.00250.0050.00750.010.01250.0150.02kept its branchchanged branchanother pairno latticeseeded 40 nodes of Lucas lattice · 10 runs per amplitude1 escape in 160 runs

Noise is not a slow rate

A stem seeded on the Lucas branch keeps it below ninety nodes per rung and abandons it above — which invites the objection that a real apex's fluctuations would knock it off regardless. Measured across a hundred and sixty runs of two independent kinds of noise, one escapes, at the amplitude where the pattern is already coming apart.

emergence · noise amplitude placement noise, at 1°2.00°field noise, at 0.015 of the barrier1.68°no noise at all0.64°largest divergence scatter still holding a latticethe two differ by 0.33° — a fifth of what either toleratesand by 2.9× more than a noiseless run scatters65 nodes per rung · 10 runs per amplitude2.00° against 1.68°

Two degrees of scatter

A lattice tolerates about two degrees of wander in its divergence angle, and two kinds of noise sharing no code agree on the number to within a third of a degree. It is not a constant: carried finer, the same stem survives 0.8°, and the tolerance tracks the band of angles that produce its pair at all.

emergence · scatter tolerance 00.50011.50-0.25000.2500.5000.750falloff exponent, log₁₀scatter, log₁₀ degrees00.50011.50-0.25000.2500.5000.750falloff exponent, log₁₀scatter, log₁₀ degreesno latticethe same lattice, whatever pevery runsome runsno runneighbourhood 12/√h · 4 runs per exponenta lattice from p ≈ 1.25 upward

The exponent that barely matters

A code comment on this site claimed since its foundation phase that the repulsion's falloff exponent hardly changes the answer. It could not be tested, because the function that would have taken it never passed one down. Tested at last, it is true on a disc — by three and a half degrees across a sixteenfold range — and on a stem it decides whether there is a pattern at all.

emergence · falloff exponent

Named alongside it

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

Divergence angleLadderNoiseRiseBranchThe placement ruleRungCylinderFibonacciMeristemMetastabilityNearest neighbour

All concepts