(*Adapted by Rafael Luís: rafaelluis@netmadeira.com
 2016-09-11: adapted for Mathematica v.10 by Ross Moore *)

(*Cobweb diagram for (Subscript[Q, c])=(x^2)+c*)

(*Function and parameters*)

Clear[c,x,x0,iterates];
f[x_,c_]:=(c+(x^2)); (*Function*)
x0=1.35;     (*initial values*)
c=-0.5;      (*parameter*)
iterates=20;

QuadracticSegments[c_,x0_,its_]:=Module[
{l=NestList[(c+#^2)&,x0,its]},
Partition[Flatten[Transpose[{l,l}]],2,1]
]

p2=Partition[QuadracticSegments[c,x0,iterates],2,1];

Manipulate[Plot[{f[x,c],x},{x,-1.5,1.5},PlotStyle->{{},Dashing[{.02}]},
Prolog->MapIndexed[{Hue[Length[#]/Length[p2]],Line[#]}&,Take[p2,2i]],
AspectRatio->Automatic,
AxesLabel->TraditionalForm/@{(Subscript[x, n]),(Subscript[x, n+1])}
],{{i,10,"iterates"},Range[Length[p2]/2]}]