A model-driven visual study of the invisible threads that organise three-dimensional chemical waves.
MOVING IMAGE — THE LIFE OF A SCROLL RINGignition 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 curtainscroll · f 1.8 · q 0.002 · ε 0.03 · ferroin
MethodThe 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.
ObservationA 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.
ReferenceA. T. Winfree, "Scroll-Shaped Waves of Chemical Activity in Three Dimensions," Science, vol.181, 937-939 (1973).
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 dishStudy #11 — BZ in a volume
The rotating corea point — the spiral tipa line — the filament, which the scroll wave wraps around
What you seethe waves themselves, painted by the catalyst's colourtranslucent shells — and a thread that exists nowhere in the fields
How it is seenlook at the dishthe medium is opaque — only computation can watch the thread itself
PARAMETERS EXPLORED
parammeaningeffect on the image
εtimescale 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
fstoichiometric factorthe core's character: 1.4 a tight core · 1.6 a meandering flower · 1.8 a clean thread
filament geometrythe initial filament — straight / ring / broken fielda vertical thread · a ring that contracts · a field that proliferates into tangles
R0initial ring radiusthe ring's lifetime — R² falls linearly in time under line tension
camerathe orbiting viewpointthe 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 curtainscroll · f 1.8 · ε 0.03 · ferroin · seed 21
the halo in the bell — a ring inside its ignition membranering · f 1.8 · ε 0.03 · R₀ 0.22 · ferroin · seed 13
nested tori — three engraved shells the ring wove around itselfring · f 1.8 · ε 0.03 · tomography · 7000 steps
a tangle — proliferating filaments as golden scriptturb · 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 itselfring · 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 cannotturb · 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).
