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The thread: Form is not mechanism

A model that reproduces a pattern has not explained it. The same spirals come out of magnetised droplets with no biology in them at all, and the actual mechanism in plants — auxin moving between cells — was worked out long after the geometry.
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 Where the angle comes from

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.

5 sides13420%6 sides45869%7 sides7311%665 bounded cellsmean 5.908 sidessix is forced, not chosen Packing and tiling

Why the average cell has six sides

Not because hexagons are efficient. Because Euler's formula leaves a tiling no choice — count the edges two ways and the mean comes out at six, whatever the cells would prefer. The efficiency argument is a different claim about a different thing.

1201301401500255075100stepdivergence angle produced at that step (°)golden anglegrowth 0.40settled spread 0.00° Where the angle comes from

Droplets with no biology in them

Douady and Couder dripped magnetised ferrofluid into a dish of silicone oil, and got spiral phyllotaxis with Fibonacci parastichy numbers out of a system containing no cells, no genes and no plant. That is the strongest evidence the pattern is physics — and the clearest warning about what a model can claim.

491 symbols · 130 segmentsa description, not a mechanism Branching and transport

L-systems describe, they do not explain

Two rewriting rules and a turtle produce something indistinguishable from a plant, and there is no plant in it — no light, no water, no auxin, no mechanics. That is worth demonstrating precisely because the output is so convincing.

0501000.2500.5000.7501growth parameter Gspread of the last 30 steps (°) — 0 means settledfilled dark: convergedthe usable range is stated, not implied Where the angle comes from

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.

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