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If this game
doesn't work on your computer, go
here
for help.
by Ed Hobbs
To operate:
Select the Preset buttons at the left to see sample patterns.
To generate your own patterns, use the digital readouts at
the right. Adjust the readouts by clicking on the digits: clicking
near the top of a digit increases its value; clicking near the bottom
decreases its value.
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.
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Explanation of Readout Values
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xFreq
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This is the number of horizontal cycles for each frame of the plot.
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yFreq
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This is the number of vertical cycles for each frame of the plot.
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hueFreq
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This is the number of hue cycles for each frame of the plot. Each
hue cycle represents a complete spectrum of colors. |
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Samples
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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). |
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