In[]:=
totals=Table[{#,Select[#,(!SKTerminated[Last[SKFixedPointEvolveList[#,2000,2000]]])&]}&[Groupings[Table[s,n],Construct2]],{n,10}];
In[]:=
ttotals=Map[Length,totals,{2}]
Out[]=
{{0,0},{1,0},{2,0},{5,0},{14,0},{42,0},{132,2},{429,41},{1430,276},{4862,1481}}
In[]:=
Text[Grid[Prepend[Table[{n,ttotals[[n,1]],ttotals[[n,2]],PercentForm[N[ttotals[[n,2]]/ttotals[[n,1]]],2]},{n,2,10}],{"size","total","nonterminating","fraction"}],FrameAll]]
Out[]=
size
total
nonterminating
fraction
2
1
0
0%
3
2
0
0%
4
5
0
0%
5
14
0
0%
6
42
0
0%
7
132
2
1.5%
8
429
41
9.6%
9
1430
276
19%
10
4862
1481
30%
In[]:=
PercentForm[.763535]
Out[]//PercentForm=
76.35%
In[]:=
#2/#1&@@@{{0,0},{1,0},{2,0},{5,0},{14,0},{42,0},{132,2},{429,41},{1430,276},{4862,1481}}
Power
:Infinite expression
1
0
encountered.
Infinity
:Indeterminate expression 0ComplexInfinity encountered.
Out[]=
Indeterminate,0,0,0,0,0,
1
66
,
41
429
,
138
715
,
1481
4862

In[]:=
N[%]
Out[]=
{Indeterminate,0.,0.,0.,0.,0.,0.0151515,0.0955711,0.193007,0.304607}
In[]:=
ListLinePlot[%]
Out[]=
2
4
6
8
10
0.05
0.10
0.15
0.20
0.25
0.30
In[]:=
sss11=ResourceFunction["ParallelMapMonitored"][(!SKTerminated[Last[SKFixedPointEvolveList[#,2000,2000]]])&,Groupings[Table[s,11],Construct2]];
In[]:=
Count[sss11,True]
Out[]=
6829
In[]:=
Length[sss11]
Out[]=
16796
In[]:=
%115/%//N
Out[]=
0.406585
sss12=ResourceFunction["ParallelMapMonitored"][(!SKTerminated[Last[SKFixedPointEvolveList[#,2000,2000]]])&,Groupings[Table[s,12],Construct2]]
In[]:=
ttimes=Monitor[Table[ResourceFunction["ParallelMapMonitored"][With[{u=SKFixedPointEvolveList[#,2000,2000]},If[!SKTerminated[Last[u]],None,Length[u]-1]]&,Groupings[Table[s,n],Construct2]],{n,12}],n];
In[]:=
ttotals={Length[#],Count[#,None]}&/@ttimes
Out[]=
{{0,0},{1,0},{2,0},{5,0},{14,0},{42,0},{132,2},{429,41},{1430,276},{4862,1481},{16796,6829},{58786,29288}}
In[]:=
#2/#1&@@@%125
Power
:Infinite expression
1
0
encountered.
Infinity
:Indeterminate expression 0ComplexInfinity encountered.
Out[]=
Indeterminate,0,0,0,0,0,
1
66
,
41
429
,
138
715
,
1481
4862
,
6829
16796
,
2092
4199

In[]:=
ListLinePlot[%]
Out[]=
2
4
6
8
10
12
0.1
0.2
0.3
0.4
0.5
In[]:=
Max[DeleteCases[#,None]]&/@ttimes
Out[]=
{-∞,0,0,1,2,4,15,15,86,894,894,1189}
In[]:=
GraphicsGrid[Partition[Table[Labeled[Histogram[DeleteCases[ttimes[[n]],None],{1},{"Log","Count"},PlotRange{{0,50},Automatic},FrameTrue],Text[n]],{n,5,12}],4]]
Out[]=
PlotLabel
In[]:=
Select[Groupings[Table[s,7],Construct2],(!SKTerminated[Last[SKFixedPointEvolveList[#,2000,2000]]])&]
Out[]=
{s[s[s]][s][s][s][s],s[s][s][s[s]][s][s]}
In[]:=
SKEvolveList[#,2]&/@{s[s[s]][s][s][s][s],s[s][s][s[s]][s][s]}
Out[]=
{{s[s[s]][s][s][s][s],s[s][s][s[s]][s][s],s[s[s]][s[s[s]]][s][s]},{s[s][s][s[s]][s][s],s[s[s]][s[s[s]]][s][s],s[s][s][s[s[s]][s]][s]}}
​
In[]:=
Select[Groupings[Table[s,8],Construct2],(!SKTerminated[Last[SKFixedPointEvolveList[#,2000,2000]]])&]
Out[]=
{s[s[s[s][s]]][s][s][s],s[s[s[s[s][s]]]][s][s],s[s[s]][s][s][s][s][s],s[s[s[s]][s][s][s][s]],s[s[s[s]][s][s]][s][s],s[s[s[s]][s]][s][s][s],s[s[s[s[s]][s]]][s][s],s[s[s[s]]][s][s][s][s],s[s[s[s[s]]][s]][s][s],s[s[s[s[s]]]][s][s][s],s[s][s][s[s]][s][s][s],s[s[s][s][s[s]][s][s]],s[s[s][s][s[s]]][s][s],s[s[s]][s[s]][s][s][s],s[s[s[s]][s[s]]][s][s],s[s[s]][s][s[s]][s][s],s[s[s[s]]][s[s]][s][s],s[s][s][s[s][s]][s][s],s[s][s][s[s[s]]][s][s],s[s[s]][s[s[s]]][s][s],s[s[s][s]][s][s[s]][s],s[s[s[s][s]]][s[s]][s],s[s[s]][s][s][s[s]][s],s[s[s[s]]][s][s[s]][s],s[s][s][s[s]][s[s]][s],s[s][s][s[s[s][s]]][s],s[s[s]][s][s[s][s]][s],s[s][s][s[s[s]][s]][s],s[s[s]][s][s[s[s]]][s],s[s][s][s[s[s[s]]]][s],s[s[s[s][s]]][s][s[s]],s[s[s]][s][s][s][s[s]],s[s[s[s]][s]][s][s[s]],s[s[s[s]]][s][s][s[s]],s[s][s][s[s]][s][s[s]],s[s[s]][s[s]][s][s[s]],s[s[s]][s][s[s]][s[s]],s[s][s][s[s][s]][s[s]],s[s][s][s[s[s]]][s[s]],s[s[s][s]][s][s[s][s]],s[s[s][s]][s][s[s[s]]]}
In[]:=
Select[SKEvolveList[#,10],LeafCount[#]8&]&/@%65
Out[]=
In[]:=
Last/@%
Out[]=
{s[s[s][s]][s][s[s]][s],s[s[s[s][s]]][s][s[s]],s[s][s][s[s]][s][s][s],s[s[s][s][s[s]][s][s]],s[s][s][s[s]][s][s[s]],s[s][s][s[s]][s[s]][s],s[s[s[s]][s]][s][s[s]],s[s[s]][s][s[s]][s][s],s[s[s]][s][s[s]][s[s]],s[s[s[s]]][s][s[s]][s],s[s][s][s[s]][s][s][s],s[s[s][s][s[s]][s][s]],s[s][s][s[s]][s][s[s]],s[s][s][s[s][s]][s][s],s[s][s][s[s][s]][s[s]],s[s[s]][s][s[s]][s][s],s[s[s]][s][s[s][s]][s],s[s][s][s[s][s]][s][s],s[s][s][s[s[s]]][s][s],s[s][s][s[s[s]][s]][s],s[s[s][s]][s][s[s]][s],s[s[s][s]][s][s[s][s]],s[s][s][s[s]][s[s]][s],s[s[s[s]]][s][s[s]][s],s[s][s][s[s]][s[s]][s],s[s][s][s[s[s][s]]][s],s[s[s]][s][s[s][s]][s],s[s][s][s[s[s]][s]][s],s[s[s]][s][s[s[s]]][s],s[s][s][s[s[s[s]]]][s],s[s[s[s][s]]][s][s[s]],s[s][s][s[s]][s][s[s]],s[s[s[s]][s]][s][s[s]],s[s[s]][s][s[s]][s[s]],s[s][s][s[s]][s][s[s]],s[s][s][s[s][s]][s[s]],s[s[s]][s][s[s]][s[s]],s[s][s][s[s][s]][s[s]],s[s][s][s[s[s]]][s[s]],s[s[s][s]][s][s[s][s]],s[s[s][s]][s][s[s[s]]]}

Looking for busy beavers