Image:Animated.gif

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No higher resolution available.

Animated.gif‎ (480 × 480 pixel, file size: 72 KB, MIME type: image/gif)

An equivalent image is now available on Wikimedia Commons as Image:Periodic identity function.gif.

[edit] Summary

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

-- Deimos 28 18:39, 12 March 2006 (UTC)

[edit] Licensing

I, the creator of this work, hereby grant the permission 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.
Subject to disclaimers.

File history

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.
Click on date to download the file or see the image uploaded on that date.

(del) (cur) 14:29, 12 March 2006 . . Deimos 28 (Talk | contribs) . . 480×480 (74,065 bytes) (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)
(del) (rev) 13:45, 12 March 2006 . . Deimos 28 (Talk | contribs) . . 480×480 (123,118 bytes) (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)