STUDY #11 · 2026 · IN OBSERVATION

BZ III — Scroll Waves

A model-driven visual study of the invisible threads that organise three-dimensional chemical waves.

MOVING IMAGE — THE LIFE OF A SCROLL RING ignition bell → curl → nested tori · f 1.8 · ε 0.03

WHAT IS THIS

In a shallow dish, the Belousov–Zhabotinsky reaction draws spirals that turn around a point. Give the medium depth, and that point stretches into a line: a filament, around which the whole three-dimensional wave — a scroll wave — rotates. The filament is invisible: it is not a substance but a phase singularity, and it behaves like a physical thread, with tension. A closed filament ring contracts and vanishes; in other regimes threads stretch and multiply into tangles.

This study extends the study #01 Oregonator engine to three dimensions and runs it in real time on the GPU. The filament is extracted each frame by a topological detector and rendered as a glowing thread inside the translucent wave volume.

one thread — a straight filament in its rotating wave curtain scroll · f 1.8 · q 0.002 · ε 0.03 · ferroin

Motif BZ reaction / scroll waves / filaments / filament tension

Method The study #01 Oregonator engine was extended to three dimensions. Scroll waves rotate around filaments — invisible line defects that the renderer extracts and draws as glowing threads inside a translucent volume. Built and modified with AI assistance; the filament geometries and the look were chosen by parameter exploration.

Observation A straight filament stands as a quiet vertical thread inside its rotating wave curtain. A closed filament ring contracts under its own line tension — measured inside this model as R² falling linearly in time — but in this confined volume the waves the ring itself sheds push back, and the thread settles into a breathing equilibrium: the thread that holds itself. In weakly excitable regimes, broken fields grow into tangles of thread.

Reference A. T. Winfree, "Scroll-Shaped Waves of Chemical Activity in Three Dimensions," Science, vol.181, 937-939 (1973).

Tools Python / NumPy / three.js / React / GLSL / ffmpeg / AI coding assistant

Year 2026

This is not a scientific simulation result, but a visual interpretation of the phenomenon.

FROM A POINT TO A LINE

The spiral's heart, given depth.

Study #01 — BZ in a dish Study #11 — BZ in a volume

The rotating core a point — the spiral tip a line — the filament, which the scroll wave wraps around

What you see the waves themselves, painted by the catalyst's colour translucent shells — and a thread that exists nowhere in the fields

How it is seen look at the dish the medium is opaque — only computation can watch the thread itself

PARAMETERS EXPLORED

param meaning effect on the image

ε timescale ratio (u vs v) the line weight — 0.02 a sharp thread ⇄ 0.05 a soft thick one. Also decides whether turbulence lives or dies

f stoichiometric factor the core's character: 1.4 a tight core · 1.6 a meandering flower · 1.8 a clean thread

filament geometry the initial filament — straight / ring / broken field a vertical thread · a ring that contracts · a field that proliferates into tangles

R0 initial ring radius the ring's lifetime — R² falls linearly in time under line tension

camera the orbiting viewpoint the tomography — a slow orbit is what makes the thread's three-dimensionality legible

Each image below records its exact parameter set.

SELECTED STILLS — 4

one thread — a straight filament in its wave curtain scroll · f 1.8 · ε 0.03 · ferroin · seed 21

the halo in the bell — a ring inside its ignition membrane ring · f 1.8 · ε 0.03 · R₀ 0.22 · ferroin · seed 13

nested tori — three engraved shells the ring wove around itself ring · f 1.8 · ε 0.03 · tomography · 7000 steps

a tangle — proliferating filaments as golden script turb · f 1.4 · ε 0.05 · noise 0.04 · tomography

SIGNATURE — THE THREAD THAT HOLDS ITSELF

A ring that should vanish, held up by its own waves.

A closed filament ring contracts under its own line tension — inside this model, its area R² falls linearly in time, and the tension flips sign as excitability weakens. Left alone, the ring should shrink to nothing.

But in this confined volume the waves the ring itself sheds reflect and push back, and the thread settles into a breathing equilibrium — nested tori engraved around a ring that refuses to die. The hero film is its whole life in one slow orbit: ignition bell, curl, the cathedral of shells.

the shells the ring wove around itself ring · R₀ 0.22 · steps 7000 · tomography

COLOUR = TOMOGRAPHY

The chemistry of colour is the same as in study #01: what you would see in a real dish is the catalyst's oxidation state, so the translucent wave shells map the oxidised-catalyst fraction (ferroin red ⇄ ferriin blue).

The filament itself is geometry, not chemistry — no molecule carries its colour — so its incandescent gold is an editorial choice, marking the one structure that only computation can see. A real 3D BZ gel is opaque: experimentalists reconstructed scroll waves by optical tomography. The rendering leans into that — translucent depth, X-ray-like shells, a bright thread.

filaments as golden script — colour marking what chemistry cannot turb · f 1.4 · ε 0.05 · tomography

Colours are artistic approximations of colours reported in the literature, not measurements. The filament's gold is editorial — the thread is invisible.

REFERENCES

A. T. Winfree. "Scroll-Shaped Waves of Chemical Activity in Three Dimensions." Science, vol.181, 937-939 (1973).

INTERACTIVE STUDY

The finished works above render the full three-dimensional volume — waves wound around an invisible line, seen as if by tomography. This is a deliberately simplified instrument, and deliberately flat: a single 2D section of that phenomenon, in which a wavefront is seeded, half of it erased, and the cut’s free ends curl into rotors — the spiral pair a scroll ring shows where it pierces a plane. Reduced in dimension, resolution, and scope, separate from the full engine that authored the works; the gold points mark where the unseen thread crosses this section.

SIMPLIFIED INSTRUMENTOREGONATOR · 2D SECTION OF A SCROLL · LIVE

This interactive study is not intended as a scientifically validated reproduction. It is a visual interpretation generated from an implemented model and curated parameter exploration — and it is a deliberately simplified instrument, separate from the full engine used to author the finished works.