s[s[s[s][s]][s[s]][s][s][s][s]]//LeafCount
In[]:=
11
Out[]=
s[s[s]][s[s]][s[s]][s][s]
In[]:=
s[s[s]][s[s]][s[s]][s][s]
Out[]=
LeafCount[%]
In[]:=
9
Out[]=
Ratios[{1,2,4,15,15,86,1109,1109,1444,6317,23679,131245}]//N
In[]:=
{2.,2.,3.75,1.,5.73333,12.8953,1.,1.30207,4.37465,3.74846,5.54267}
Out[]=
ListStepPlot[%]
In[]:=
Out[]=
{{2,0,s[s]},{3,0,s[s][s]},{4,1,s[s][s][s]},{5,2,s[s][s][s][s]},{6,4,s[s][s][s][s][s]},{7,15,s[s[s[s]]][s][s][s]},{8,15,s[s[s[s[s]]][s][s][s]]},{9,86,s[s[s]][s[s]][s[s]][s][s]},{10,1109,s[s[s][s]][s[s]][s][s][s][s]},{11,1109,s[s[s[s][s]][s[s]][s][s][s][s]]},{12,1444,s[s[s]][s[s]][s[s][s][s][s][s]][s]},{13,6317,s[s[s]][s[s]][s[s][s][s][s][s][s]][s]},{14,23679,s[s[s]][s[s]][s[s][s][s][s][s][s][s]][s]},{15,131245,s[s[s]][s[s]][s[s][s][s][s][s][s][s][s]][s]}}
CombinatorFixedPoint[s[s[s]][s[s]][s[s][s][s][s][s]][s]]
In[]:=
Out[]=
CombinatorExpressionGraph[CombinatorEvolve[s[s[s]][s[s]][s[s][s][s][s][s]][s],200],AspectRatio.25,"ShowVertexLabels"False]
In[]:=
Out[]=
CombinatorExpressionGraph[%248,AspectRatio.25,"ShowVertexLabels"False]
In[]:=
Out[]=
CombinatorFixedPointList[s[s[s]][s[s]][s[s][s][s][s][s]][s]]//Length
In[]:=
1445
Out[]=
Differences[LeafCount/@CombinatorFixedPointList[s[s[s]][s[s]][s[s][s][s][s][s]][s]]]
In[]:=
Out[]=
Histogram[%256,{1},{"Log","Count"}]
In[]:=
Out[]=
Max[%256]
In[]:=
14
Out[]=
Position[%256,14]//Flatten
In[]:=
{5,296,585,872}
Out[]=
CombinatorExpressionGraph[CombinatorEvolve[s[s[s]][s[s]][s[s][s][s][s][s]][s],#],AspectRatio.25,"ShowVertexLabels"False]&/@{5,296,585,872}
In[]:=
,
,
,
Out[]=
CombinatorExpressionGraph[CombinatorEvolve[s[s[s]][s[s]][s[s][s][s][s][s]][s],700],AspectRatio.25,"ShowVertexLabels"False]
In[]:=
Out[]=
Non LO Champions
Non LO Champions
cases=Complement[Groupings[Table[s,7],Construct2],{s[s[s]][s][s][s][s],s[s][s][s[s]][s][s]}]
In[]:=
Out[]=
lens=ResourceFunction["ParallelMapMonitored"][Length[CombinatorFixedPointList[#,{"Leftmost","Innermost",1}]]&,cases]
In[]:=
{1,1,1,1,2,1,1,1,1,1,2,2,3,3,1,1,1,1,2,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,4,4,3,4,4,5,5,1,1,1,1,2,1,1,1,1,1,2,2,3,3,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,2,2,3,3,2,2,2,2,3,2,2,2,2,2,3,3,4,4,3,4,3,3,4,4,5,5,6,5,4,5,6,6,3,3,4,8,5,4,5,5,5,5,10,6,11,7,5,6,6,7}
Out[]=
Samples of behavior
Samples of behavior
Log scale
Log scale
Linear
Linear
Termination Test
Termination Test