Concept

Nearest neighbour — where it appears

4 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
21 and 34 spiralscounted, not assumed

Counting the spirals

Almost every claim about phyllotaxis is a claim about how many spirals run through a pattern, and the count is almost never done. It can be done from the points alone, by machinery that is never told what angle built them — and then a count of 34 is evidence rather than a restatement.

lattices · counting
00.2500.5000.7501120130140150divergence angle (°)closest pair, as a fraction of the mean spacing (higher is better)137.508°400 points per anglethree criteria, three winners

Packing, measured four ways

The claim is that the golden angle packs best. It is measurable, and the measurement gives three different winners on three criteria — all near 137.5° and none of them it. That does not make the claim wrong; it makes the usual statement of it wrong.

tissue · packing
4 chains · counted pair 4 and 62-jugate at 69.35° · rise 0.064 chains in this family

Counting 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.

lattices · chain counting
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.

RiseCylinderDivergence angleBranchNoiseParastichyAsymptotic claimCounting blindChain countingCriterion dependenceDiscriminationEnsemble

All concepts