Lyapunov Fractal

Watch Lyapunov Fractal live in the browser

Smooth gold shapes with fine contour lines, often called swallows, lie against a deep blue night scattered with faint stars. A thin bright seam traces the border between them, and the view drifts slowly through the picture, breathing between a wide view and a close-up.

The image is Mario Markus's Lyapunov fractal of the logistic map x → r·x·(1 − x), where r alternates between two values a and b in a fixed pattern such as AABAB. Each pixel is one (a, b) pair, and its Lyapunov exponent says whether the orbit settles, drawn in gold, or turns chaotic, drawn in blue. The preset moves through eight A/B patterns, cross-fading each into the next, and smooths every music signal so the picture never jerks.

What it reacts to

• Bass: warms and brightens the gold regions
• Spectrum: the stable regions glow in bands, each degree of stability tied to one frequency band
• Treble: stars twinkle in the deepest chaos
• Kick drum: lights the edge between order and chaos, and every few kicks a new A/B pattern fades in
• Loudness: drives the drift through parameter space and the slow palette shift; silence freezes them

Tune

Kicks per change sets how many kicks pass before a new A/B pattern, Drift scales how fast the view wanders, and Gold sets the colour of the stable regions.

Music that suits it

Music with a steady kick and warm bass, such as deep house, techno or downtempo, brings regular pattern changes while the gold glows evenly.

How to play it

Install Deus, play music on Spotify, YouTube Music, Yandex Music or any other tab and click the Deus icon on that tab. Then pick Lyapunov Fractal in the WebGL presets, or press ← → on the page until it comes up.