A Lissajous figure is the graph of a system of parametric equations
x = A sin(at + α)
y = B sin(bt + β)
which describe complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch (an American mathematician remembered for his work on ocean navigation) in 1815, and later in 1857 by Jules Antoine Lissajous (a French physicist).
Lissajous figures are sometimes used in graphic design as logos. Examples include the Australian Broadcasting Corporation and the Disney’s Movies Anywhere. They have also been used in modern art, for instance the Dadaist artist Max Ernst painted Lissajous figures directly by swinging a punctured bucket of paint over a canvas.
I coded Lissajous figures in Processing, a flexible software sketchbook and a language for learning how to code within the context of the visual arts. Inspired by Generative Gestaltung book (a wonderful text to learn generative design in Processing and p5.js), I connected close points on the figure with transparent lines. Some unexpected patterns emerged:
Then I modified the equations as follows (can we still call them Lissajous curves?):
x = A sin(at + α) cos(ct)
y = B sin(bt + β) cos(dt)
After a long and exhausting search over the infinite parameter space, some ancestral figures emerged:
Probably the most disquieting one that I found was the following. When I showed it to my old mother she immediately said: Le na zevita! (it’s an own!, in Venetian dialect). So I decided to name it Lissajous zevita!
