In[]:=
StyleRowReverseMap​​Labeled[ArrayPlot[#,ImageSize->{Automatic,1.5Length[#]}],Style[Length[#]-5,Italic,"Text",12]]&,Last/@KeysGroupBy
,Sort[​​{#,Reverse/@#}]&[CellularAutomaton[{#[[1]],2,2},{{1},0},#[[2]]+5]]&,LineSpacing->{1,15}
Out[]=
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In[]:=
Out[]=
{977937844307,450504084307,4137297300215,2999618996215,513199396181,1813663652181,2586455476166,2658796948166,989234468164,1757030308164,437708068156,1213876132156,3665692052150,2586486708150,1917756852136,383173924136,1390061460136,1612345252136,3133812148118,3201967508118,1144699684117,1182173540117,3530171828107,2457511316107,989497236107,2058233268107,307684644103,1079666596103,2452268980101,3531474324101,1044040996100,1320832420100,142584360497,191893906097,266300152496,319566994096,205376859690,44739112490,312633896487,259680811687,152506510884,202025563684,246049374883,152136235683,299447234083,84698869283,105448386083,31301010083,98632850083,98110862883,191539752482,245777346082,353017234082,139110133282,98086224481,122017578081,299320258077,353842933277,255656901276,255761755676,85341176476,84922565276,245996946075,296091790875,30977360474,293090544474,283076848474,107756944474,151745525273,147945208473,242615286871,312414402071,299185142871,363947819671,265658717268,202758696468,265240106068,205538245268,105658101267,98842565267,245724917266,145507317266,191984786066,349661790866,245066282065,296095067665,242181878865,44630162065,97478392465,353371128465,97481654864,245538141264,125160797264,171719210062,31214314062,94545642061,125109187661,205561182859,243077266059,95384565259}
In[]:=
middlerep[list_]:=MapAt[1-#&,list,Round[Length[list]/2]]
In[]:=
pertevol[rule_,t_,tp_]:=Module[{all=CellularAutomaton[{rule,2,2},{{1},0},t+1],top},top=CellularAutomaton[{rule,2,2},First[all],tp];ArrayPlot[Join[Most[top],CellularAutomaton[{rule,2,2},middlerep[Last[top]],t+1-tp]]]]
In[]:=
pertevol[3665692052,151,50]
Out[]=
In[]:=
pertevol[3665692052,151,150]
Out[]=

Characterize the notion of “preserving the same idea”...

[ Generate the dendrogram based on appearances ]