Harmonograph Simulation and Mathematical Drawing
Primary Source: https://www.karlsims.com/harmonograph.html
Author: Karl Sims · Year: 2012 · Publisher: Karl Sims Media & Simulation Archive
Summary
Karl Sims’ documentation and interactive simulation of mechanical harmonographs—drawing machines utilizing coupled pendulums whose damped harmonic oscillations create complex geometric Lissajous curves and visual harmonies.
Key Points
- Coupled Harmonic Motion: Multiple independent pendulums oscillating at distinct frequencies, phases, and decay rates generate intricate geometric drawings.
- Mathematical Drawing Machines: Physical 19th-century mechanical drawing devices translated into real-time computational trigonometry and parametric equations.
- Visualizing Resonance and Damping: Illustrates energy dissipation and acoustic ratios (intervals like fifths, octaves) through spatial curves.