Plot fractals for superior iteration of complex logistics maps.

Question

I am trying to generate fractals from complex logistics maps as stated in Generation of fractals from complex logistic map by Agarwal and Rani. I am using Mann iteration of complex logistics maps.

It says that The maps have been plotted using (r x , r y , b)

Here, we have given some of the superior fractals generated from complex logistic map using superior iterations, in C programming language

I am not sure how those fractals have been plotted. Can somebody give me the pseudo code for it?

Answer 1

Thanks to Prof. @Mark McClure I was able to plot the fractal.

The code is in R.:

B = 1
cols <- colorRampPalette(c("blue","yellow","red","black"))(5)
xmin = 0.3
xmax = 0.5
nx = 400
ymin = -0.2
ymax = +0.2
ny = 400
n=200
rx=3.57
ry=0
px=0.1
py= 0
x <- seq(xmin, xmax,by=0.0001)
y <- seq(ymin, ymax,by=0.0001)
c <- outer(x,y*1i,FUN="+")
p <- matrix(c, nrow=length(x), ncol=length(y))
k <- matrix(0.0, nrow=length(x), ncol=length(y))
for (rep in 1:n) {
  index <- which(Mod(p) <= (2/B))
  px = Re(p[index])
  py = Im((p[index]))
  pxt = B*(rx*(px - px*px + py*py)- ry*(py - 2*px*py)) + (1-B)*px
  pyt = B*(rx*(py-2*px*py) + ry*(px - px*px+py*py)) + (1-B)*py
  px = pxt
  py = pyt
  p[index] = px + py*1i;
  k[index] <- k[index] + 1
}
image(x,y,k, col=cols)