File:Mandelbrot Creation Animation.gif
Summary[edit]
Description 
An animated diagram showing iterations of the equation used to generate the Mandelbrot set, a fractal first studied by Benoît Mandelbrot in 1979. The animation shows the values of Z for first 20 iterations of the equation where c is a complex variable. Mandelbrot set graphics are usually generated using the socalled "escape algorithm", where color is assigned according to the number of iterations it took for the equation to diverge past a preset limit, and black color is used for regions that never diverge. This, however, is a plot of a much simpler quantity: the actual values of the equation at the first 20 iterations. Every pixel in the image corresponds to a different value of a complex constant c ranging from 2.2 to 1 on the real axis (horizontal) and from 1.2i to 1.2i on the imaginary axis (vertical). Z is initialized to 0. At each iteration, the next value of Z is calculated using the equation above. This graphic was generated with 13 lines of code in the R language (see below for the code). For each point, the magnitude (aka absolute value) of Z is calculated, than scaled using an exponential function to emphasize fine detail, and finally mapped to color palette (jetColors). Dark red is a very low number, dark blue is a very high number. The deep blue region "squeezing" in the boundaries of the fractal is the region where Z value diverges to infinity. 
Date  
Source  Own work 
Author  Jarekt 
Other versions  
GIF development  Rspluslibrary(caTools)
jet.colors = colorRampPalette(c("#00007F", "blue", "#007FFF", "cyan", "#7FFF7F", "yellow", "#FF7F00", "red", "#7F0000"))
m = 600
C = complex( real=rep(seq(1.8,0.6, length.out=m), each=m ),
imag=rep(seq(1.2,1.2, length.out=m), m ) )
C = matrix(C,m,m)
Z = 0
X = array(0, c(m,m,20))
for (k in 1:20) {
Z = Z^2+C
X[,,k] = exp(abs(Z))
}
write.gif(X, "Mandelbrot.gif", col=jet.colors, delay=100)

Licensing[edit]
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 FrontCover Texts, and no BackCover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. 

This file is licensed under the Creative Commons AttributionShare Alike 4.0 International, 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license.  
Attribution: Jarekt  

File history
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Date/Time  Thumbnail  Dimensions  User  Comment  

current  18:32, 13 June 2007  600 × 600 (1.78 MB)  Jarekt (talk  contribs)  {{Information Description=Animation GIF file showing iteration of creating Mandelbrot set image Source=selfmade Date=06/13/2007 Author= Jarekt }} Image generated using R language and executing the following code: library(caTools) jet 
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