To operate:
Select the Pre-set 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'
set-up 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 colourful designs.
Explanation of Readout Values
xFreq
This is the number of horizontal cycles for each frame of the
plot.
yFreq
This is 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 colours.
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).
