Concept

Initial condition — where it appears

3 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
137.5°disorder 3177°8 peaksdisorder 747°8 peaksdisorder 11109°7 peaksdisorder 19151°7 peaksdisorder 2347°7 peaksdisorder 31133°8 peaksthe angle a spiral would need to repeatsix runs, identical equationsspread 129°

A ring cannot make a spiral

The peaks on a Turing ring do not all appear at once — there is a first and a second. But which two lead is decided by the starting disorder, so the angle between them comes out at 177°, then 47°, then 109°, then 151°. A divergence angle is a relationship that repeats, and this one does not.

mechanism · ring limit
10011012013014011.502falling rise, as −log₁₀divergence the stem is producing (°)137.51°, Fibonacci99.50°, Lucasseeded at 99.50°, rise 0.127/11 against 8/13

The rate decides the branch

Forty nodes of Lucas lattice, carried down to the same fine rise twice. Hurried, the pattern holds the Lucas ladder through three more forks at 99.5°. Given room, it abandons it at the first fork it reaches and walks to 8/13 at 137.5°. Same seed, same rise, two ladders — with a threshold between them at about ninety nodes per rung.

emergence · branch choice
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

Named alongside it

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

RiseBifurcationBranchFibonacciLadderRepulsionAttractorCensusContinuityConvergenceCritical rateCylinder

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