Animation of Cobweb Diagrams for the Logistic Mapwith(plots): with(plottools):anim:=proc(b,x0,N) local k,pg,z1,u,z,lg,F;
F:=(x,b)->b*x*(1-x);
#Set up the graph of F(x,b) as a background plot:
pg:=plot([x,F(x,b)],x=0..1,color=black,linestyle=4,title=cat("b= ",convert(b,string)));
#Set up the iteration trajectory as an animation:
u:=x0; z1:=[u,0];
lg[0]:=CURVES([z1]);
for k from 1 to N do
z:=F(u,b); z1:=z1,[u,z],[z,z]; u:=z;
lg[k]:=CURVES([z1])
od;
display([seq(lg[k],k=0..N)],insequence=true);
#Finally display the animation and background together:
display({pg,%})
end:anim(4,.45,100);#Try any other reasonable values of b, x0 and N.