> f:=(lmd,x)->4*lmd*x*(1-x); #Define the Logistic family.

[Maple Math]

> with(plots):

> p1:=plot({[1,0],[1,1]},x=0..1,y=0..1):p2:=plot(x,x=0..1,y=0..1):p3:=plot(1,x=0..1,y=0..1): # Plot the box 0<=x<=1,0<=y<=1 and the diagonal y=x.

> lmd:=3/4:iterate1:=plot(f(lmd,x),x=0..1,y=0..1,color=green):iterate2:=plot(f(lmd,f(lmd,x)),x=0..1,y=0..1,color=black):display({p1,p2,p3,iterate1,iterate2}); # Plot the first and the second iterates of f for a given `lmd'.

> lmd:=3.8/4:iterate3:=plot(f(lmd,f(lmd,f(lmd,x))),x=0..1,y=0..1,color=black):display({p1,p2,p3,iterate3}); # No period-3 points yet for 'lmd'<3.8/4.

>