zn(z,c,p,k) = 1 + c*z*exp({0,1}*(p + k/(1.0+abs(z)**2)))

colors = "web-green web-blue orange dark-salmon"
c = 0.9
p = 0.4
set xrange [-1:2.5]
unset key
set size square
set samp 20000
set term pngcairo enh font ",8" size 480,480
set out "ikeda_complex.png"

set multiplot layout 2,2
do for [i=1:4] {
  zp = {0,0}
  k = - 4 - i*2
  set title sprintf("k = %.2f", k) font ",10"
  plot '+' u (zc = zn(zp,c,p,k), real(zc)):\
            (zp = zc, imag(zc)) w d lc rgb word(colors,i)
}
unset multiplot