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