File:Animated plot of the first five successive partial Fourier series.gif

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Animated_plot_of_the_first_five_successive_partial_Fourier_series.gif (480 × 480 pixels, file size: 72 KB, MIME type: image/gif, looped, 5 frames, 2.5 s)

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Date 12 March 2006 (original upload date)
Source Transferred from en.wikipedia to Commons.
Author Deimos 28 at English Wikipedia

Licensing

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Deimos 28 at the English-language Wikipedia, the copyright holder of this work, hereby publishes it under the following license:
w:en:Creative Commons
attribution share alike 		This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Subject to disclaimers.
Attribution: Deimos 28 at the English-language Wikipedia
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.
This licensing tag was added to this file as part of the GFDL licensing update.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. Subject to disclaimers.

Source code

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This file was created by me using the following R source code: 

f=function(x) {return((x+pi)%%(2*pi)-pi)}
x=c(-3000:3000)*pi/1000
y=f(x)
b=function(n){return((-1)**(n+1)*2/n)}
y_fourier=function(n) {return(sin(x%*%t((1:n)))%*%b(1:n))}

for(i in 1:5) {
jpeg(paste("animated_",i,".jpg",sep=""))
plot(x,y,type="p",col="green", pch=".",main="Periodic version of the identity function", axes=FALSE,xlab="",ylab="")
lines(rep(pi,201),(-100:100)*pi/100,lty="dotted")
lines(rep(-pi,201),(-100:100)*pi/100,lty="dotted")
axis(side=2, pos=0,at=c(-1,1)*pi,font.axis=5,labels=c("-p","p"))
axis(side=1, pos=0,at=c(-3:3)*pi,font.axis=5,labels=c("-3p","-2p","-p","0","p","2p","3p"))
lines(x,y_fourier(i))
dev.off()
}

Then using the following shell command: 

$ convert -delay 50 -loop 50 ani*.jpg animated.gif

Original upload log

[edit]
The original description page was here. All following user names refer to en.wikipedia.
Date/Time Dimensions User Comment
2006-03-12 14:29 480×480× (74065 bytes) Deimos 28 Created by me using R with the following source code: {| |- f=function(x) {return((x+pi)%%(2*pi)-pi)} |- |x=c(-3000:3000)*pi/1000 |- |y=f(x) |- |b=function(n){return((-1)**(n+1)*2/n)} y_fourier=function(n) {return(sin(x%*%t((1:n)))%*%b(1:n))} |for(i in 1
2006-03-12 13:45 480×480× (123118 bytes) Deimos 28 This file was created by me using the following [http://wwwr-project.org R] source code: f=function(x) {return((x+pi)%%(2*pi)-pi)} x=c(-3000:3000)*pi/1000 y=f(x) b=function(n){return((-1)**(n+1)*2/n)} y_fourier=function(n) {return(sin(x%*%t((1:n)))%*%b(1

File history

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Date/TimeThumbnailDimensionsUserComment
current14:52, 8 August 2017Thumbnail for version as of 14:52, 8 August 2017480 × 480 (72 KB)BD2412 (talk | contribs)Transferred from en.wikipedia

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