Spirograph
Draw harmonograph patterns from motion and frequency ratios
Explore how frequency ratios, phase and damping shape a harmonograph drawing. Layer traces to compare patterns and create artwork.
Key idea
A harmonograph combines oscillating motions into a trace. Frequency ratios influence repetition, phase changes the alignment of the motions, and damping gradually reduces their amplitude. Similar-looking curves can come from different settings.
Try this first
Choose a preset and let the trace develop before changing its settings. Compare a simple ratio with a slightly detuned one, then adjust damping. Watch how the path’s symmetry and persistence change over time.
How to get started
- Set the X and Y frequencies, or pick a musical ratio.
- Press Draw to set the pendulums in motion.
- Add layers and change their colors.
Explore a little further
Try another experiment
Keep a simple frequency ratio and compare two phase settings. Then restore the phase and change damping. Separate changes to the shape of the path from changes to how tightly it winds toward the center.
Good to know
The drawings are generated by the selected motion model. A visually complex trace need not imply a complicated numerical ratio, and a changing trace may need time to reveal its structure.
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