Mathematical animations in pure Python — zero dependencies, one file, stdlib only.
No pygame. No numpy. No shaders. Just tkinter, math, and ideas that are older than computers: fiber bundles, chaotic attractors, hyperbolic geometry, n-body gravity. If you have Python, you already have everything this needs.
python spectral_geometry.py # windowed art / ambient display
python spectral_geometry.py --selftest # headless render test, no screen neededControls: Space / → / mouse click — next scene · ← — previous · Esc / Q — quit. Scenes auto-rotate every 7 minutes. Live clock + optional system telemetry (CPU/RAM, if psutil is present) make it a pleasant second-monitor ambient panel.
 Hopf Fibration — the circles of S³ stereographically projected to 3D: nested tori breathing as the base sphere rotates. The crown jewel of the collection. |
 Three-Body Ballet — the Chenciner–Montgomery figure-8 choreography: three equal masses under real gravity (velocity-Verlet), weaving one shared orbit from nothing. |
 Hyperbolic Flow — a geodesic web in the Poincaré disk carried by a live Möbius transformation. Escher's Circle Limit, but flowing. |
 Clifford Attractor — a strange attractor whose four parameters breathe sinusoidally: the form perpetually reborn. |
 Chaos Butterflies — 36 double pendulums differing by 10⁻⁵ radians: a minute of unison, then sensitive dependence tears them apart. The theorem, drawn. |
 Klein Bottle — a rotating non-orientable surface (bagel immersion) with a breathing scale. |
 Torus Knot Morph — (2,3) → (3,4) → (2,5)… knots smoothstep-morphing into one another. |
 Murmuration Wars — three boid flocks locked in rock-paper-scissors predation; a caught bird converts to the hunter's colour in a burst ring. |
Because constraints are the art. Every scene here is:
- One file, no installs — runs on any Python ≥ 3.10 with tkinter (the default on Windows/macOS, one package away on Linux)
- A pooled-canvas renderer — pre-allocated line items, style caching, quantized HSV: thousands of segments at 30 fps on an office laptop
- Honest mathematics — real Verlet gravity, real RK4 pendulums, real Möbius maps and stereographic projections; nothing is a pre-baked path
spectral_geometry.py # the current piece: 8 scenes, windowed, selftest
series/ # the evolution: 01→09, fullscreen tkinter experiments
assets/ # GIF/poster previews + the headless renderer that made them
The series/ folder is the archaeology — nine earlier screensavers (sacred geometry, 4D polytopes, walking creatures, wireframe terrain…) that led here. assets/render_previews.py re-renders every preview headlessly (Pillow used only for asset generation, never at runtime).
MIT — take it, remix it, put it on the second monitor of your open-space office.