NestGraph[x{3n+1,2n+2}

In[]:=

Solve[4x(1-x)xp,x]

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x1-1+

1

2

1-xp

,x1

2

1-xp

In[]:=

ListPlot[With[{a=2},Catenate[MapIndexed[{#1,-First[#2]}&,NestList[Flatten[{1/a(1-Sqrt[1-#]),1/a(1-Sqrt[1+#])}]&,{.5},5],{2}]]],PlotRangeAll]

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In[]:=

ListPlot[With[{a=1},Catenate[MapIndexed[{#1,-First[#2]}&,NestList[Flatten[{Sin[#],Cos[#]}]&,{.5},5],{2}]]],PlotRangeAll]

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In[]:=

NestGraph[{Sin[#],Cos[#]}&,{.5},3]

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In[]:=

Plot[{Sin[x],Cos[x]},{x,0,1}]

Out[]=

In[]:=

ListPlot[With[{a=1},Catenate[MapIndexed[{#1,-First[#2]}&,NestList[Flatten[{#,1-#}]&,{.3567},5],{2}]]],PlotRangeAll]

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In[]:=

Plot[1-2Abs[1/2-x],{x,0,1}]

Out[]=

In[]:=

ListPlot[With[{a=1},Catenate[MapIndexed[{#1,-First[#2]}&,NestList[Flatten[{1-2Abs[1/2-#],2Abs[1/2-#]}]&,{.3567},10],{2}]]],PlotRangeAll]

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In[]:=

NestGraph[{1-2Abs[1/2-#],2Abs[1/2-#]}&,1/3,5]

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In[]:=

ListPlot[With[{a=1},Catenate[MapIndexed[{#1,-First[#2]}&,NestList[Flatten[{FractionalPart[2#],FractionalPart[3#]}]&,{.3567},10],{2}]]],PlotRangeAll]

Out[]=

In[]:=

NestList[Union[Flatten[{FractionalPart[2#],FractionalPart[3#]}]]&,{.3567},10]

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{{0.3567},{0.0701,0.7134},{0.1402,0.2103,0.4268},{0.2804,0.4206,0.6309,0.8536},{0.2618,0.5608,0.7072,0.8412,0.8927},{0.1216,0.4144,0.5236,0.6781,0.6824,0.7854},{0.0343,0.0472,0.2432,0.3562,0.3648,0.5708,0.8288},{0.0686,0.0944,0.1029,0.1416,0.4864,0.6576,0.7124,0.7296},{0.1372,0.1888,0.2058,0.2832,0.3087,0.3152,0.4248,0.4592,0.9728},{0.2744,0.3776,0.4116,0.5664,0.6174,0.6304,0.8496,0.9184,0.9261,0.9456},{0.1328,0.2348,0.2608,0.5488,0.6992,0.7552,0.7783,0.8232,0.8368,0.8522,0.8912}}

In[]:=

Length/@%

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{1,2,3,4,5,6,7,8,9,10,11}

In[]:=

Length/@NestList[Union[Flatten[{FractionalPart[2#],FractionalPart[3/2#]}]]&,{.3567},10]

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{1,2,3,6,8,12,16,21,32,46,64}

In[]:=

ListPlot[With[{a=1},Catenate[MapIndexed[{#1,-First[#2]}&,NestList[Flatten[{FractionalPart[2#],FractionalPart[3/2#]}]&,{.3567},10],{2}]]],PlotRangeAll]

Out[]=