Concept

Convergence — where it appears

4 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
05e+51e+62e+60100200300angle around the boundary (°)repulsion from what is theregrowth 0.40 · 14 elements in playthe minimum is where the next one goes

The angle is an output

137.5° is not a constant of nature. It is where a rule settles — a rule that places each new element as far as it can from the ones already there, contains no reference to the golden ratio, and reaches the same answer from starting angles a hundred and sixty degrees apart.

emergence · attractor
0501000.2500.5000.7501growth parameter Gspread of the last 30 steps (°) — 0 means settledfilled dark: convergedthe usable range is stated, not implied

Where the model stops

Below a growth parameter of about 0.18 this implementation does not converge — the settled angle wanders over a hundred degrees however long the run. That is the range where the literature says the interesting behaviour lives, and it is worth a figure rather than a quietly chosen axis.

emergence · modellimit
grown from a coarse start100.0%divergence chosen at random10.8%share ending on a consecutive Fibonacci pair16 grown runs, starting divergences from 67° to 299°every one of them ended on 8/1367 nodes per rung · rise 0.4 → 4.8e-3100% against 10.8%

Continuity from a coarse start

At a fine rise, one divergence in seven gives a Fibonacci pair. Grow a stem from a coarse start at a divergence nobody chose, down to that same rise, and sixteen runs out of sixteen end on 8/13. The expansion phase's interpretation was that continuity does the work; this is the measurement it never had.

emergence · continuity
-8-6-4-20distance from the tip, in node spacingsvariation ÷ nearest shell, log₁₀0–22–44–88–1616–3232–64a golden-angle stem at a rise of 0.004 · shells in units of √hnearest shell dominates by 1.1× at p = 0.5, 9733× at p = 3

How far a primordium reaches

The placement rule's repulsion falls as an inverse cube because that is what two magnetised droplets do, and nothing about a plant supplies the exponent. Asking what it controls produced one tidy wrong answer and one measured right one — and the difference between them is the difference between a total and a variation.

emergence · interaction range

Named alongside it

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

RepulsionBranchFibonacciMeristemAttractorDivergence angleLadderRiseTruncationBifurcationCensusContinuity

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