Simulation of a harmonograph, a device which draws Lissajous figures based on the periodic motion of a pencil over a spinning table.
To try this
simulation:
Use the sliders to control the horizontal and vertical speed of the pencil, as well as the spinning speed of the table. Press the "Erase Board" button to erase the current drawing.
What's Going On?
The harmograph consists of a suspended platform which can swing in any direction. The pen traces out a path that describes the sum of all motions of the table. If the X axis and Y axis motions of the table were equal, a circle would be drawn on the paper. If the table is set in motion with unequal X and Y axis motions, patterns called Lissajous figures, such as those illustrated here, are produced. Setting the platform in motion with a combination of oscillating and twisting motions produce the most interesting images owing to the more complicated motions of the platform.
There's More!
The kind of patterns shown here occur in nature. For example, the moon traces out a curve as it moves around the earth. As the earth orbits the sun, the pattern gets more complex. And as the sun moves around the center of our galaxy, the path the moon takes becomes astonishingly similar to the patterns you can make here. Mathematicians study patterns like these to better understand and describe the complicated motions of planets, satellites, machines and weather systems.
