File:Tent map.gif

\[Mu] = 1.9;
tent[x_] := \[Mu] Min[x, 1 - x];
val = NestList[tent, 0.4, 500];
p0 = Table[
   Show[
    Plot[tent[x], {x, 0, 1}, PlotStyle -> {Thick, Black}, AxesLabel -> {"\!\(\*SubscriptBox[\(x\), \(n\)]\)", "\!\(\*SubscriptBox[\(x\), \(n + 1\)]\)"}, LabelStyle -> {Black, Bold}, PlotLabel -> "Tent map: \!\(\*SubscriptBox[\(x\), \(n + 1\)]\)=\[Mu] \min{\!\(\*SubscriptBox[\(x\), \(n\)]\),1-\!\(\*SubscriptBox[\(x\), \\(n\)]\)}"]
    ,
    Graphics[{Red, Thick, Opacity[0.2], Table[{Line[{{val[[j]], 0}, {val[[j]], val[[j + 1]]}}], Line[{{val[[j]], val[[j + 1]]}, {0, val[[j + 1]]}}]}, {j, 1, k, 1}]
      }]
    ]
   , {k, 1, 300}];
ListAnimate[p0]

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