Epicycle 🌀

Epicycle is a generalised roulette generator: chained rotating arms, each driven by a clock or governed by real physics, tracing a pattern one pen stroke at a time. Named after Ptolemy's model of the heavens, nested circles-on-circles piled up to fit what was observed. This app leans into that idea rather than avoiding it: an arm can be a perfect deterministic gear, or a genuine simulated body whose motion nobody dictated in advance, and the two mix freely in one chain.

⚙️ How It Works

• Build a chain of arms. Each one anchors to the tip of the arm before it.
• Set each arm to Driven (a fixed speed and shape) or Simulated (a spring or pendulum that responds to the chain's own motion and gravity).
• Watch the pen head trace the result, and reshape the chain live to see the pattern change in real time.

✨ Key Features

🔗 Arm chains Circles, ellipses, polygons, and the Superformula for flower and star shapes. Speed and radius can be set absolutely or relative to the arm before it, with ratios compounding down the chain.

🌱 Real simulation Spring-mass and rigid-pendulum arms carry their own state frame to frame. Push a pendulum far enough and the chain turns chaotic; nobody scripted where it goes.

🌊 Evolve & Modulate LFOs (six waveforms, locked to sim time or the wall clock) and slow Brownian drift can target almost any parameter on any arm, or global values like centre drift and trail thickness.

💫 Particles Emit from the pen head with independent control over direction and speed. Direction can follow the pen's own motion, sit perpendicular to it, or spray outward from the arm's own pivot.

🎨 Colour & look A draggable Colour by Age gradient ramp, plus an optional 3D Tube mode that renders the trail as a lit, swept mesh in seven finishes instead of a flat line.

🔍 Auto Zoom Fit everything ever drawn, or stay tight on just the last few seconds, so a slow-drifting or ever-growing pattern never wanders out of frame.

🌗 Light & Dark themes.

No goals, no timers, no wrong answers. Just the chain, finding its own shape.

🧮 The maths and credits, for anyone curious

Epicycle's classical arms are the real Ptolemaic model. Ptolemaic Mars uses Mars's actual sidereal period and orbital distance, scaled for the screen, and genuinely reproduces retrograde loops. The flower and star shapes come from the Superformula, a single equation published by Johan Gielis in 2003 that generalises the circle, the ellipse, and a huge range of natural forms under one parameterisation. The simulated arms integrate a plain spring-mass or rigid-pendulum model at a fixed timestep, so their physics is genuine.

The seven matte finishes available in 3D Tube mode are converted from Blender's own bundled MatCaps, released CC0 / public domain by the Blender community.