Generator

two-noises-one-tolerance

The largest divergence scatter at which a run is still a lattice, from each kind of noise at the largest amplitude that leaves one. The two routes share no code below the placement rule: one displaces the node after the choice, the other perturbs the energy the choice is made over. They agree to 0.66°.
A lattice survives about 1.6° of scatter, whichever way the noise arrivesThe largest divergence scatter at which a run is still a lattice, from each kind of noise at the largest amplitude that leaves one. The two routes share no code below the placement rule: one displaces the node after the choice, the other perturbs the energy the choice is made over. They agree to 0.66°.placement noise, at 1°1.97°field noise, at 0.015 of the barrier1.31°no noise at all0.64°largest divergence scatter still holding a latticethe two differ by 0.66° — a fifth of what either toleratesand by 2.6× more than a noiseless run scatters65 nodes per rung · 3 runs per amplitude1.97° against 1.31°

Drawn at its defaults, in noise, and where it gets in. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 5 essays

the blast radius of changing it

Where the angle comes from

A pattern with a rate

Every lattice on this site is a static object indexed by a parameter, and a plant is not. Put the rise on a clock, place each node where the repulsion from the ones below it is least, and the object that comes out has a history — which is the first thing here that could disagree with the ladder.

Where the angle comes from

Two degrees of scatter

A lattice tolerates about two degrees of wander in its divergence angle, and two kinds of noise sharing no code agree on the number to within a third of a degree. It is not a constant: carried finer, the same stem survives 0.8°, and the tolerance tracks the band of angles that produce its pair at all.

Where the angle comes from

Where the noise gets in

Ninety runs of noise applied after the rule has chosen, and not one changes branch. Fifty-six of noise applied to the choice itself, and one does. Only a disturbance upstream of the decision can restructure which nodes are neighbours of which — which is what a branch is.

Stems and cones

The sequence has a memory

Every measurement this collection has made of a stem's divergence angles throws the order away. A spread is invariant to shuffling. Put the angles back in order and there is a large correlation between one and the next — 0.54 with no noise at all — which is the rule correcting itself, and which nothing had looked at.

Where the angle comes from

The boundary belongs to the pattern

Three kinds of noise, in three incommensurable units, destroy a lattice at the same place — about a degree and a half of divergence scatter. The previous phase measured that of two kinds and called it a scale rather than a constant. With a third it looks less like a coincidence and more like a property of what a lattice is.

All 105 generators