Brusselator: a chemical oscillator as a phase-plane trail — Classical Chaos

The Brusselator is a theoretical autocatalytic chemical oscillator from Ilya Prigogine and the Brussels school (the name is from Brussels). On Classical Chaos it is continuous well-mixed ODEs: Euler-integrate the rates, then paint (x, y) as a trail in the phase plane. Spatial reaction–diffusion — the BZ dish movie, spots on a grid — is a different kind of viz.

Equations

Defaults sit at a = 1, b = 3, dt = 0.02, seed (1, 1).

One forward-Euler step per sample:

const dx = a - (b + 1) * x + x * x * y
const dy = b * x - x * x * y
x = x + dx * dt
y = y + dy * dt

dt gets clamped so the step stays sane. If |x| or |y| blow past about 100, the state gets clamped too.

Color walks the trail in hsl chunks; the tip often reads yellower than the older path.

What the trail shows

With a = 1, b = 3 the path looks closed. Concentrations chase each other along that cycle and do not settle to a quiet point. Smaller b changes how the path sits and how it settles.

Full canvas

On the full Brusselator stage twist a / b / dt (about [0.1, 3], [0.1, 5], [0.001, 0.1]), try the example presets (1, 3, 0.02), (1, 2.5, 0.02), and (0.5, 1.2, 0.02), scrub how long the trail is, and drag to rotate the view. The trail rebuilds from (1, 1).