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

(*Cobweb for an exponential Map*)

(*Function and parameters*)

Clear[r,x,x0,iterates];
f[x_,r_]:=(r+1+ Exp[-4*π](x^(-2)-1))^(-0.5); (*Function*)
x0=0.001;     (*initial values*)
r=0;      (*parameter*)
iterates=20;

f[x,0]

LogisticSegments[r_,x0_,its_]:=Module[
{l=NestList[(r+1+ Exp[-4*π](#^(-2)-1))^(-0.5)&,x0,its]},
Partition[Flatten[Transpose[{l,l}]],2,1]
]

p2=Partition[LogisticSegments[r,x0,iterates],2,1];

Manipulate[Plot[{f[x,r],x},{x,0,1.1},PlotRange->{0,1.1},PlotStyle->{{},Dashing[{.02}]},
Epilog->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]}]