Initial condition — where it appears
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.
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.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
RiseBifurcationBranchFibonacciLadderRepulsionAttractorCensusContinuityConvergenceCritical rateCylinder