BZK 1.0: The Excitable Baseline

A Greenberg–Hastings excitable CA, nucleation and autocatalytic propagation, classified honestly

The trunk of the Belousov-Kernel lineage. This is a Greenberg–Hastings excitable cellular automaton reproducing the Belousov–Zhabotinsky phenomenon: a quiescent medium in which pacemaker sites nucleate and fire, then recruit their neighbours autocatalytically into outward target waves and, where a wavefront breaks, rotating spirals. Each cell cycles resting → excited → refractory → resting. A resting cell excites when enough excited neighbours surround it; an excited cell cannot re-fire until it has passed through its refractory tail.

Everything here supplies exactly two kernel primitives, T0-P (resting ≠ excited, a threshold-gated directional transition) and T0-σ (neighbour recruitment). It supplies none of the rest of ignition: no T0-M closure, no T0-B identity-bearing boundary, no MBC self-paid maintenance. Turn off the pacemakers and the pattern relaxes to quiescence. The readout below refuses to call any of this ignition, a nucleation is a triggered wave, not an I-Pop, and calling it one would be the BAEP category error. This is the honest before-picture Stage B will try to move.

This field is run using isotropic neighbour weighting.

The basin, and whose basin it is

Once it is running with the feed ON, the medium settles into a persistent regime of target waves and rotating spirals. That regime is a basin: push the field and, as long as the feed continues, the activity climbs back to roughly the same level and the wave pattern re-forms. Press Perturb (wipe patch) to knock out a square of the field and watch what happens, either neighbouring waves flood back in and the basin recovers, or the hole widens and the activity falls and it ruptures. The wave activity readout is the fraction of cells currently excited; the basin regime label reads that fraction against its recent history and reports one of three states, Quiescent, Active regime, or Collapsing.

But read the honest part: this basin is not the structure’s own. It is held open from outside by the pacemaker feed. Turn Feed OFF and perturb, and the basin does not defend itself, the waves drain and the field relaxes to quiescence, because nothing here pays its own maintenance (no MBC), holds an identity-bearing boundary (no T0-B), or closes a recursive loop (no T0-M). So the recovery you see with feed ON is a supplied recovery, the substrate handing the order back, not the structure re-producing it. That distinction, an externally-fed basin versus a self-paid one, is the whole question the Belousov-Kernel lineage exists to move. BZK 2.0 (Stage B) will test whether a region can hold this basin with the feed OFF.

What this is, and is not

This page reproduces a known result (Greenberg–Hastings excitable media, the CA analogue of BZ trigger waves) and classifies it against the kernel. It is experimental, downstream, and non-canonical: it applies canonical constraints and does not modify them. The next experiment, BZK 2.0 (Stage B), will add a self-maintained boundary and recursive closure and test whether an ignited region can hold identity through the refractory period. Per § 14.3 negative-results discipline, a failure there is a valid result about the mechanism, not a failure of the kernel.