What is a Harmonograph?

A harmonograph is a mechanical drawing device that uses swinging pendulums to create intricate geometric patterns. As the pendulums move back and forth, they control the motion of a pen across paper, producing flowing curves known as Lissajous figures. Because the motion gradually slows due to friction, each drawing evolves over time, creating complex, organic patterns that visually reveal the mathematics of harmonic motion.

Today’s Harmonograph:

(Click to restart)

What happens every day?

Because the pattern is generated from a mathematical function, it’s possible to create a completely new harmonograph every day. A scheduled job on my server randomly generates the parameters for the harmonograph equations, computes the resulting curve, and renders it into an animated GIF.

Each day the server:

• Generates a new set of harmonic motion parameters
• Calculates the curve point by point
• Draws the pattern progressively into an animated GIF
• Publishes the new harmonograph and archives the previous

Below are all the harmonographs that have been created! Which one is your favorite?