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)