Thursday, December 8, 2011

Lissajous curves

And after the Epitrochoids, we're going to see another family of wonderful figures: The Lissajous curves. The equations that describe these curves are the following

the curves vary with respect the parameter t and their appearance is determined by the ratio a/b and the value of δ.
As usual, I made a snippet to visualize them:
from numpy import sin,pi,linspace
from pylab import plot,show,subplot

a = [1,3,5,3] # plotting the curves for
b = [1,5,7,4] # different values of a/b
delta = pi/2
t = linspace(-pi,pi,300)

for i in range(0,4):
 x = sin(a[i] * t + delta)
 y = sin(b[i] * t)

This is the result
and setting delta = pi/4 the we have
while, if we set a = [1,2,2,1], b = [5,8,1,2] and delta = 0.709 the result is


  1. It is a beautiful thing to see these patterns on an oscilloscope.

  2. Thanks a lot. Very useful article.

  3. Hi.

    I wonder if I could use a spanish free translation of some of your articles (of course, with attribution) in a possible future blog of scientific python (in spanish and if I find some time).

  4. Hi basuradek,
    you can consider every post released under CC BY-NC-SA 3.0 licence. So, feel free to publish the translation of the my posts but you have to link the original versions on this website.

    By the way, I would love to see some of my work translated in Spanish. If you'll do it, let me know :)


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