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I was playing around with R tonight, and came across a tight little bit of code on the WIkipedia page for R, to generate a Mandelbrot set. It is below. I needed to lighten up a few of the loops and variables, (it threw an error at 250mb vector size initially, but I'm sure there is a memory setting somewhere to crank up if you're keen on the resolution.

**## Source Code **from http://en.wikipedia.org/wiki/R_(programming_language) - second example (I modified a couple of the variables to not crash my old laptop)

library(caTools) # external package providing write.gif function

jet.colors <- colorRampPalette(c("#00007F", "blue", "#007FFF", "cyan", "#7FFF7F",

"yellow", "#FF7F00", "red", "#7F0000"))

setwd("C:/Users/Home/Documents/R/Mandelbrot")

#m <- 1200 # define size - MODIFIED TO LIGHTEN UP

m <- 800 # went smaller because 171mb vector size error-ed out

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 MODIFIED TO 10 - ERROR WENT AWAY

for (k in 1:10) { # loop with to see if smaller better - 10 ok; 15 too much

Z <- Z^2+C # the central difference equation

X[,,k] <- exp(-abs(Z)) # capture results

}

write.gif(X, "Mandelbrot.gif", col=jet.colors, delay=1000)

## gif is multi-image, be patient if you just see a blob to begin

# Background on the Mandelbrot Set

The **Mandelbrot set** is a mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes), and is named after the mathematician Benoit Mandelbrot, who studied and popularized - **Source:** http://en.wikipedia.org/wiki/Mandelbrot_set

- The Mandelbrot set is defined as the set of all points such that the above sequence does
*not*escape to infinity. - the Mandelbrot set is just a set of complex numbers. A given complex number
*c*either belongs to*M*or it does not. A picture of the Mandelbrot set can be made by colouring all the points that belong to*M*black, and all other points white. The more colourful pictures usually seen are generated by colouring points not in the set according to how quickly or slowly the sequence diverges to infinity

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Created: July 25, 2014

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