contents Lissajous Lab explore

To operate: Click the Preset buttons at the left to see sample patterns. To make your own patterns, use the digital readouts at the right. Click near the top of a digit to increase its value; click near the bottom to decrease its value.

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Explanation of Readout Values
xFreq the number of horizontal cycles for each frame of the plot.
yFreq the number of vertical cycles for each frame of the plot.
hueFreq This is the number of hue cycles for each frame of the plot. Each hue cycle represents a complete spectrum of colors.
Samples This is the number of line segments which will be used to draw each frame of the plot. Increasing this number will make the curves appear smoother. Decreasing this number will exacerbate the aliasing in the plot (making it look more like string art than a mathematical curve).

Lissajous Figures

Lissajous (pronounced LEE-suh-zhoo) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows.

Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.

Lissajous figures often appeared as props in science fiction movies made during the 1950's. One of the best examples can be found in the opening sequence of The Outer Limits TV series. ("Do not attempt to adjust your picture--we are controlling the transmission.") The pattern of criss-cross lines is actually a Lissajous figure.

The Lissajous Lab provides you with a virtual oscilloscope which you can use to generate these patterns. (You will control the horizontal. You will control the vertical.) The applet also allows you to apply a signal to modulate the hue of the trace, so you can create colorful designs.

The Lissajous Lab and description were created by Ed Hobbs. He graciously allows reposting of his Lissajous Lab. (We are sorry that his homepage seems to have disappeared from the Web recently, so we can no longer find him or link to him!!)

Copyright 1997-2000 Edward R. Hobbs