mirror-lattice
Drawn at its defaults, in two organs taken away, not one. It takes no options at all, so every essay calling it gets this exact drawing.
Called by 6 essays
the blast radius of changing it
A period the grid invented
A wrecked stem was reported as settling into a repeating block of three angles — 219.84°, 220.31°, 220.78° — which is the smaller of its two spiral counts and would have confirmed a standing prediction. Those three numbers are three consecutive samples of the azimuth grid. There is no block; there is a constant the grid cannot write down, and the routine that found the block was working perfectly.
Where the angle comes fromA rule that cannot heal a hole
The placement rule corrects itself against a displacement — that is what the lag-one correlation of −0.6 has been saying since it was measured. It does not correct itself against a deletion. Which organ is removed decides whether the stem is back on its lattice in twenty-four organs or never, and the boundary between the two is sharp, reproducible and in the middle of the front.
Where the angle comes fromThe pattern the cut leaves behind
A stem that never recovers from a removal is not disordered. Its divergences settle into a cycle of eight angles and repeat it exactly for the rest of the run, and a counter reading the positions calls the result 8/16 — a two-jugate lattice. The rule has a second attractor at the same growth parameter, and an ablation is how you get to it.
Where the angle comes fromA front with no middle
Take one organ out of a stem and the pattern sometimes never comes back — but that was measured on a front thirteen organs wide, where five of the thirteen offsets are beyond repair. Repeat it on a front of five and every single ablation heals. The band that cannot be undone is not a number the rule carries; it is what two fixed edges leave over.
Where the angle comes fromA cut of two organs
One organ removed from a stem is felt out to the larger parastichy number and no further, and at the coarsest arrangement the stem always repairs itself — so the one rung where the interesting prediction could be checked had no experiment that could reach it. Two organs can. The second cut brings a parameter with it, and that parameter turns out to be a control.
Where the angle comes fromThe stem that changed hands
A stem that never recovers from an ablation is supposed to end up somewhere worse than it started — a repeating block of angles, a pattern with the wrong counts in it. At the coarsest arrangement it ends up somewhere that is not worse at all: at 220.3125°, which is 360° minus the divergence it was cut from. The lattice is intact and its handedness is reversed.