Mandelbrot_seq.r

library(caTools)  # external package providing write.gif function
jet.colors = colorRampPalette(c("#00007F", "blue", "#007FFF", "cyan", "#7FFF7F", 
                               "yellow", "#FF7F00", "red", "#7F0000")) 
m = 4000     # 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)) # initialize output 2D array
for (k in 1:20) {  # loop with 20 iterations
   Z = Z^2+C    # the central difference equation 
   X[,] = exp(-abs(Z)) # capture results
   write.gif(X, paste("Mandelbrot", k, ".gif"), col = jet.colors)
}