Spirograph

Motion & Curves

The curve a pen traces through a hole in a small gear rolling inside a ring — a hypotrochoid — drawn live on the Super Nintendo and driven with the joypad. Written in C and compiled to a real .sfc ROM with the llvm-mos-based 65816 toolchain (16-bit accumulator, +mos-a16). Each point is a sin/cos lookup plus two fixed-point multiplies; the figure blooms stroke-by-stroke into a bitmap canvas in WRAM. Cycle through four curve families — hypotrochoid, epitrochoid, rose and Lissajous.

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↑/↓ ring · ←/→ wheel · Q/W pen · X/A family · Shift preset · Enter reset

Click the screen, then play. The rose draws itself in over a second or two; change a dial and it re-blooms — tab away and it pauses.

Controls

Keys	Action
`↑ / ↓`	Ring radius R + / −
`← / →`	Wheel radius r − / +
`Q / W`	Pen offset d − / +
`X / A`	Next / previous curve family
`Shift`	Cycle gear preset
`Enter`	Reset

The four curve families

Cycle them with X (next) / A (previous) — each re-blooms the canvas. The on-screen HUD shows the live R (ring), W (wheel), D (pen) and the petal count.

Family	What it is
HYPOTROCHOID	pen inside the wheel as it rolls inside the ring — the classic rosette
EPITROCHOID	wheel rolls outside the ring — a ring of interlocking loops
ROSE	rhodonea ρ = cos(kθ) — a k-petalled flower
LISSAJOUS	x = sin(aθ+δ), y = sin(bθ) — the crossing-wave figure

Tips

The bloom is the point. Each new sample is line-connected to the last, so the figure draws itself; nudging ↑↓/←→/QW changes the gear and re-blooms a fresh curve.
Gear presets (Shift) jump between classic Spirograph wheel/ring sets — each a different petal count (ring ÷ gcd of ring and wheel).
It's a compiler stress-test. The whole point is the sin/cos-LUT + fixed-point-multiply inner loop and the gear-ratio divide — exercising the 65816 16-bit-accumulator codegen.

Written in C with an LLVM/65816 SNES toolchain and verified pixel-for-pixel against two emulators (MAME + bsnes-jg). The player above is that exact cycle-accurate core — hit Verify fidelity to reproduce the build gate's WRAM assert (curve-math hash 0x32D4) live in this tab. No far pointers, so the same program is checked five ways: host == default == +mos-a16 == +mos-xy16.