Harmonograph / Lissajous Art Screensaver
A harmonograph is a real Victorian-era drawing machine where two or more pendulums, each swinging at a slightly different frequency, combine their motion through a linked pen to trace intricate looping curves. This screensaver simulates that exact real physics — two virtual pendulums, gradually losing energy to friction, tracing a decaying spiral of loops.
How the Harmonograph / Lissajous Art screensaver works
Two simulated pendulums each swing along their own axis at their own real frequency and phase, exactly like a real physical harmonograph's independent pendulums.
Their combined x and y motion, sampled continuously, traces the drawn curve — the same Lissajous-style combination principle real harmonographs use.
Real friction is simulated too: each pendulum's amplitude decays slowly over time, so the traced curve spirals inward rather than repeating forever.
Small differences between the two pendulums' frequencies are what produce the rich, looping rosette patterns rather than a simple ellipse.
A worked example
Watch the curve begin as wide, sweeping loops and gradually tighten into a dense, intricate rosette near the center as the simulated pendulums lose real energy — then the canvas clears and a fresh curve begins.
Settings & tips
- Line color recolours the traced curve.
- Each fresh curve rolls new random pendulum frequencies, so no two runs look alike.
- Watch closely early on — the initial wide loops reveal the frequency ratio most clearly.
Frequently asked questions
- Is a harmonograph a real machine?
- Yes — real Victorian-era harmonographs used physical swinging pendulums linked to a pen to draw curves exactly like these, and hobbyists still build them today.
- Why do the loops shrink over time?
- Real friction is simulated — each pendulum's swing amplitude decays gradually, exactly as it would on a real physical machine.
- Is a key needed?
- No — it's a pure local computation.
- Is it free?
- Yes — free, no download, in your browser.