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# Tag Archives: Graphics Interchange Format

## A Missing Mandelbrot Who Dun It

December 12, 2010 12:29 pm / Leave a comment

I had tried recreating this .gif using #catools in a windows environment, but the resolution was not quite good. it seems package catools is dependent on Operating System,

Anyway, there are two approaches to creating this code- one is given at

http://blog.revolutionanalytics.com/2010/09/mandelbrot-set.html

and is simply

library(caTools) # external package providing write.gif function jet.colors = colorRampPalette(c("#00007F", "blue", "#007FFF", "cyan", "#7FFF7F", "yellow", "#FF7F00", "red", "#7F0000")) m = 600 # define size 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) # reshape as square matrix of complex numbers Z = 0 # initialize Z to zero X = array(0, c(m,m,20)) # initialize output 3D array for (k in 1:20) { # loop with 20 iterations Z = Z^2+C # the central difference equation X[,,k] = exp(-abs(Z)) # capture results } write.gif(X, "Mandelbrot.gif", col=jet.colors, delay=100) The other approach is from http://rtricks.blogspot.com/ and also suggests who the original author of this fascinating Mandelbrot gif was - apparently it was created in 2005 and is 5 years old ### Reproduced from http://tolstoy.newcastle.edu.au/R/help/05/10/13198.html### Written by Jarek Tuszynski, PhD.

library(fields) # for tim.colors library(caTools) # for write.gif m = 400 # grid size 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)) } image(X[,,k], col=tim.colors(256)) # show final image in write.gif(X, "Mandelbrot.gif", col=tim.colors(256), delay=100)

`and finally- this time I used Linux /Ubuntu 10`

`and got the colors correct- just happy to find who created the original image`

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`Of course 2010 had its share of notable deaths- `

`Benoit Mandelbrot passed away this year`

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###### Related Articles

- Mandelbrot Set, evolved (revolutionanalytics.com)
- “Fractals, Chaos Theory and the Butterfly Effect: Benoit Mandelbrot is dead. By Geniusofdespair” and related posts (eyeonmiami.blogspot.com)
- Benoit Mandelbrot, father of fractals, dies at 85 (go.theregister.com)
- The Beautiful Fractals of the Late Benoit Mandelbrot [Video] (gawker.com)

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