STUDY #04 · 2026 · IN OBSERVATION

BZ II — Thermal Fields

A model-driven visual study of one chemistry split into many regimes by heat.

MOVING IMAGE — SKY / SEA tfield step · Ea 4 · Ea_f −2

WHAT IS THIS

Temperature is the invisible conductor of the BZ reaction. A chemical reaction's rate follows the Arrhenius law — warm faster, cold slower — so in a dish that is not the same temperature everywhere, the oscillation runs at different speeds in different places. You never see the temperature itself; you only see what it does to the waves: their wavelength, the bending of their fronts, where their sources gather.

This study takes #01's Oregonator reaction–diffusion system and multiplies its reaction rate by a prescribed temperature field. Where a region's stoichiometry is also made temperature-dependent, its whole pattern regime shifts — so a single canvas can hold turbulence and calm at once. The temperature field is treated as a frozen landscape given from outside; the reaction runs on top of it.

sky over sea — step temperature seam step · horizon 0.62 · Ea 4 · Ea_f −2

Motif BZ reaction / Oregonator with a temperature field / phase & wave-speed gradients

Method The study #01 GPU (GLSL) reaction–diffusion engine was extended with an Arrhenius temperature field that modulates the local reaction rate — and, where a region's stoichiometry is temperature-dependent, its pattern regime. Built and modified with AI assistance; the geographies and the look were chosen through parameter exploration. The moving pieces animate the temperature field itself while the waves keep running.

Observation One medium reads as many worlds — a churning warm sky over a calm cold sea, chirped targets, pacemaker spots, organic geographies. Hotter means a faster clock, a shorter wavelength, and a thinner, sharper line. Colour follows temperature, not a catalyst.

Reference S. Arrhenius, "Über die Reactionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren," Zeitschrift für Physikalische Chemie, vol.4, 226-248 (1889); J. J. Tyson & P. C. Fife, The Journal of Chemical Physics, vol.73, 2224-2237 (1980).

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.

PARAMETERS EXPLORED

param meaning effect on the image

tfield temperature-field shape step: a sky/sea two-phase world · radial: rings tightening toward the warm centre · spots: pacemakers · blobs: organic thermal geography · gradient: a wavelength chirp

Ea Arrhenius sensitivity of the clock larger values widen the hot⇄cold speed difference — a stronger wavelength gradient

Ea_f temperature-dependent stoichiometry pushed negative, hot regions turn turbulent while cold regions go still — the main lever behind the sky/sea density contrast

T_lo / T_hi temperature range the range of speeds inside one field — the pressure range of the pen

horizon / seam step position & boundary width the sky-to-sea ratio, and how hard the coastline is

morph animating the temperature field the landscape drifts and the waves re-solve around it — the core of the moving pieces

Each image below records its exact parameter set.

SELECTED STILLS — 5

sky over sea step · horizon 0.62 · Ea 4 · Ea_f −2

high horizon — a wide swelling sea step · horizon 0.76 · Ea 4 · Ea_f −2

chirped target rising radial · Ea 4 · Ea_f −2

organic thermal geography blobs · Ea 4 · Ea_f −2

COLOUR = TEMPERATURE

Study #01 coloured the field by the catalyst's oxidation state. This study changes the logic: here hue comes from the invisible temperature. A cold steel-blue ice and a hot ember orange sit at the two ends of the field.

The wave amplitude sets the luminance, and the crest lifts toward white-hot. So the thermal geography reads as colour while the chemistry reads as light — which is what lets the same medium look like a warm sky over a cold sea.

The palette is an artistic mapping of an abstract temperature, not a measured colour.

organic thermal geography — warm ridges, cold valleys blobs · Ea 4 · Ea_f −2

Palette ice_ember — hue = temperature · luminance = wave amplitude · crest → white-hot.

REFERENCES

S. Arrhenius, "Über die Reactionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren," Zeitschrift für Physikalische Chemie, vol.4, 226-248 (1889).
J. J. Tyson & P. C. Fife, "Target patterns in a realistic model of the Belousov-Zhabotinskii reaction," The Journal of Chemical Physics, vol.73, 2224-2237 (1980).
R. Luther, "Räumliche Fortpflanzung chemischer Reactionen," Zeitschrift für Elektrochemie, vol.12, 596-600 (1906).

INTERACTIVE STUDY

A small window into the model behind this study — a deliberately simplified instrument, reduced in resolution, scope, and rendering. The finished works above are something else entirely: parameters swept, frames chosen, and graded by hand from the full engine. Slide the horizon and the heat, and watch one chemistry split into two worlds.

SIMPLIFIED INSTRUMENTOREGONATOR × ARRHENIUS · LIVELENS — TEMPERATURE FIELD

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.