fx(a,x,n) = 0 < n ? fx(a,a*(1-x)*x,n-1): a*(1-x)*x

set term pngc font "Arial,10" size 480,480
set out "multi_logistic.png"
set xrange [2.5:4]
set yrange  [0:1]
unset key
set samples 100
set tics tc bgnd      # bgnd : background color
N = 1000

set multiplot
do for [i = 0:N] {
if (i == N) { set tics tc rgb "black" } 
a = 2.5 + 1.5/N*i
xa = fx(a,0.8,200)
plot '+' u (a):(fx(a,xa,$0)) w dots
}
unset multiplot

! display "multi_logistic.png"