Indexing the archive…
Your Universe of Digital Possibilities
An excitable medium does nothing until you push it over a threshold — then it fires, then it sits refractory, unable to fire again until it recovers. Break a wavefront and the free end curls around its own refractory tail and rotates forever: a spiral wave. It is the same mathematics as a re-entrant cardiac rotor — a spiral pinned in heart muscle is tachycardia; when it breaks into many wavelets it is fibrillation — and as the chemical waves of the Belousov–Zhabotinsky reaction. Spawn one, then break a planar front in its own tail to make your own.
A fast excitable variable v with a cubic nullcline, coupled to a slow recovery w. A small kick decays; a kick past threshold fires a full spike, then a refractory pause — the engine of every wave here. (Simulated via Barkley’s numerically-robust cousin.)
One stable rest state and a threshold. Below it perturbations die; above it the response is all-or-none and identical however hard you pushed, followed by a recovery window in which it cannot fire again. Threshold plus refractoriness is the whole secret.
Diffusion D and reaction rate r set how fast an excitation front marches — faster coupling, faster wave. Multiply by the recovery period T and you get the wavelength: the spacing between crests in a train, or the arms of a spiral.
A curved wavefront travels slower than a flat one by an amount set by its curvature κ. A broken end lags, the front pivots about the gap, and the lag winds it into a spiral that turns forever about its tip — why spirals are inevitable, not accidental.
The Spiral is the rack’s study in excitability — a threshold plus a refractory tail, emergent in space and time. It sits one step along from The Skin (INST·06), whose reaction–diffusion settles into a steady Turing pattern that never propagates; here the same two-field machinery instead travels. It is the spatial cousin of The Chorus, whose phase oscillators synchronise with no space at all — give an oscillator a medium to live on and you get a rotating wave. It is The Contagion’s wavefront made continuous, and a sibling of The Flow as a field PDE. We integrate the Barkley model — the numerically-robust cousin of the FitzHugh–Nagumo kinetics shown in the cards — so the front never blows up under explicit Euler. The stakes are not abstract: a single pinned rotor in heart muscle is a tachycardia, its breakup into wavelets is fibrillation, and the same spirals sweep the cortex as spreading depression behind a migraine aura.