An interactive generative-art piece: a strange attractor — a single point governed by four constants — is iterated millions of times and rendered as the accumulated density of its wandering. It never repeats, never escapes. The image is not drawn; it is deposited, like silt from moving water.
一个交互式生成艺术作品。一个点,被四个常数支配,迭代上百万次——永不重复、永不逃逸;它游走的密度沉积成图像。换个种子,就是另一个宇宙。
- Every seed is guaranteed alive. Before rendering, each seed's four constants are run through a Lyapunov-exponent test (
assets/inline). Only genuinely chaotic systems (λ > 0.45) pass; thin, collapsed, line-like attractors are silently rejected and re-rolled. So you can spin the seed dial forever and never hit a dud. - Density, not lines. A point's visitation count per pixel becomes light. A per-render integer lookup table maps millions of accumulated hits to color in real time — faint filaments and dense caustics coexist without one drowning the other.
- Reproducible. The same seed always yields exactly the same universe, forever. The sidebar even shows you the equations and the Lyapunov exponent of the universe you're looking at.
- It develops. The attractor accumulates progressively over a couple of seconds, like a photograph surfacing in a tray.
- Hosted: enable GitHub Pages (Settings → Pages → Source: GitHub Actions, or Deploy from branch → main) → live at
https://<you>.github.io/strange-equilibria/. - Locally: just open
index.html. No build step, no server. The only dependency is p5.js from a CDN.
| Control | What it does |
|---|---|
| Seed | Selects the universe (its four constants). Prev / Next / Random / type-a-number. |
| Density | How many millions of iterations accumulate — richness vs. speed. |
| Contrast | Tone curve on log-density — lifts faint filaments or deepens to stark ink. |
| Fill | How much of the frame the attractor occupies. |
| Rotation | Spins the composition. |
| Colors | Paper (background), Ink (filaments), Glow (dense cores). Try a dark paper + bright ink for a luminous, nebula look. |
| Download PNG | Saves the current 1200×1200 frame. |
The engine is a De Jong attractor:
x′ = sin(a·y) − cos(b·x)
y′ = sin(c·x) − cos(d·y)
A seed deterministically picks (a, b, c, d) in [-3, 3], gated by the Lyapunov test so the dynamics are truly chaotic. A short pre-pass measures the attractor's bounds (so it's framed well); then a single point is iterated, and each landing increments a density buffer. Density → color happens through a log-compressed, gamma-corrected lookup table for speed. Reproducibility comes from seeding p5's RNG; nothing is left to chance that shouldn't be.
The aesthetic philosophy behind the movement is in PHILOSOPHY.md — and there's a quiet idea woven into it: a strange attractor is the geometry of bounded unpredictability — any system that is governed but not foretold. You don't need to know that to enjoy it; you'll just feel a restless order.
strange-equilibria/
├── index.html # the whole piece — algorithm, UI, p5.js (self-contained)
├── PHILOSOPHY.md # the algorithmic manifesto
├── README.md
├── LICENSE
└── docs/ # (optional) put a preview.png render here
Built with p5.js. Structure and styling follow Anthropic's algorithmic-art viewer template. Strange attractors trace back to Peter de Jong's iterated maps and the broader study of chaotic dynamical systems.
MIT. Make prints, fork the math, build your own universes.