Wednesday, April 18, 2007

Mandelbrot Set with R Animation

A few days ago I had the opportunity of having dinner with BenoƮt Mandelbrot
when he gave a seminar talk at the Bu Mathematics and Statistics Department. At the same time I was trying to find a way to produce animation in R. I came across this great post which was relevant for both purposes.

Using the code

### Reproduced from
### 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)

we get the following animation


adam said...

Looks great. Could you explain the algorithm , what it does in the M-set interior ?

makeyourownmandelbrot said...

A blog about the Mandelbrot set accompanying an ebook designed for school-level readers - it'll take you from basic arithmetic, through the idea of iteration, give a very gentle introduction to complex numbers, and hold your hand through coding your own Mandelbrot and Julia sets.

Comments welcome on both the blog and the ebook (published soon) - the aim is to maximise understanding and I believe anyone with school maths can do it.

Sorry to post here but I hope people will find it through your excellent post about the Mset.