Risto A. Paju
Lissajous figures are a convenient source of smooth curves for
algorithmic artists. I have used them for fixed shapes as well as
paths for moving objects, and even for moving the point of view.
This film presents an inside view of the curve x = sin(2t + 0.1); y
= sin(3t + 0.337); z = sin(5t). While I originally adjusted the
parameters for visual harmony only, this curve turned out to be a
Lissajous knot, and it inspired me to learn more about knots in
general. The braided style of the latter half is also related to
Lissajous figures. Regular flat braids can be realized as 2D
Lissajous curves with the third dimension as the free variable t,
and the tube braid shown here is likewise based on sinusoids with
phase offsets. To show the front seat view, the camera follows the
curve with t proportional to real time. The speed of propagation
dl/dt is then turned into engine noise, using MIDI pitch bend
commands sent to a synthesizer.