## 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)
subplot(2,2,i+1)
plot(x,y)

show()
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).