File:Fourier31.gif

 

This plot was created with Matplotlib.

The separate pictures was made with this program (fourier.py):

#!/usr/bin/env python
# coding: utf-8
from __future__ import division

import pylab
from pylab import show, plot, linspace
from pylab import zeros
from pylab import sin, pi

def fourier(n=15):
    x = pylab.linspace(-pi, pi, 1024)
    y = pylab.zeros(1024)
    pylab.grid(False)
    pylab.hold(False)
    for i in range(1,n+1,2):
        y += sin(i*x)/i
    pylab.plot(x,4/pi*y, "b")
    pylab.title(u"Fourier series approximation of square wave, %02d addends" %n)
    pylab.savefig("fourier%02d.png" % n)
    #pylab.show()

if __name__ == "__main__":
    for i in range(1,33,2):
        fourier(i)

Then thise pictures was unified with ImageMagick into one gif as follows:

  convert -delay 30 -loop 0 *.png fourier.gif

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You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/3.0CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 truetrue