Out[]=
{s[s][s],s[s[s]],s[s][k],s[s[k]],s[k][s],s[k[s]],s[k][k],s[k[k]],k[s][s],k[s[s]],k[s][k],k[s[k]],k[k][s],k[k[s]],k[k][k],k[k[k]]}
In[]:=
Length/@SKFixedPointEvolveList/@AllCombinators[3]
Out[]=
{1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1}
In[]:=
Length/@SKFixedPointEvolveList/@AllCombinators[4]
Out[]=
{2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,3,2,1,1,1,3,2,1,1,1,3,2,1,1,1,3,2,1,1,1,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,2,2,2,1,2,2,2,2,1,2,2,2,2,1,2,2,2,2,1,2}
In[]:=
Select[AllCombinators[4],Length[SKFixedPointEvolveList[#]]3&]
Out[]=
{s[k][s][s],s[k][s][k],s[k][k][s],s[k][k][k]}
In[]:=
SKFixedPointEvolve/@%
Out[]=
{s,k,s,k}
In[]:=
Grid[Transpose[SKFixedPointEvolveList/@{s[k][s][s],s[k][s][k],s[k][k][s],s[k][k][k]}],FrameAll]
Out[]=
s[k][s][s] | s[k][s][k] | s[k][k][s] | s[k][k][k] |
k[s][s[s]] | k[k][s[k]] | k[s][k[s]] | k[k][k[k]] |
s | k | s | k |
In[]:=
Histogram[%,{1}]
Out[]=
In[]:=
Length/@SKFixedPointEvolveList/@AllCombinators[5]
Out[]=
{3,2,1,1,3,1,1,1,2,1,2,1,1,1,3,2,1,1,3,1,1,1,2,1,2,1,1,1,4,2,1,1,3,1,1,1,2,1,2,1,1,1,4,2,1,1,3,1,1,1,2,1,2,1,1,1,4,3,1,2,4,1,1,1,3,1,2,2,1,1,4,3,1,2,4,1,1,1,3,1,2,2,1,1,4,3,1,2,4,1,1,1,3,1,2,2,1,1,4,3,1,2,4,1,1,1,3,1,2,2,1,1,3,2,2,1,3,2,1,1,3,2,3,1,1,1,3,2,2,1,3,2,1,1,3,2,3,1,1,1,3,2,2,1,3,2,1,1,3,2,3,1,1,1,3,2,2,1,3,2,1,1,3,2,3,1,1,1,3,2,2,2,3,2,1,1,3,2,3,2,1,1,3,2,2,2,3,2,1,1,3,2,3,2,1,1,3,2,2,2,3,2,1,1,3,2,3,2,1,1,3,2,2,2,3,2,1,1,3,2,3,2,1,1,2,2,2,1,2,1,2,1,2,1,2,2,2,2,2,2,2,1,2,1,2,1,2,1,2,2,2,2,2,2,2,1,2,1,2,1,2,1,2,2,2,2,2,2,2,1,2,1,2,1,2,1,2,2,2,2,2,3,2,2,2,1,2,1,2,1,2,2,2,2,2,3,2,2,2,1,2,1,2,1,2,2,2,2,2,3,2,2,2,1,2,1,2,1,2,2,2,2,2,3,2,2,2,1,2,1,2,1,2,2,2,2,3,2,3,1,3,2,2,1,2,2,2,2,2,2,3,2,3,1,3,2,2,1,2,2,2,2,2,2,3,2,3,1,3,2,2,1,2,2,2,2,2,2,3,2,3,1,3,2,2,1,2,2,2,2,2,2,3,2,3,2,3,2,2,1,2,2,2,2,2,2,3,2,3,2,3,2,2,1,2,2,2,2,2,2,3,2,3,2,3,2,2,1,2,2,2,2,2,2,3,2,3,2,3,2,2,1,2,2,2,2,2,2}
In[]:=
Select[AllCombinators[5],Length[SKFixedPointEvolveList[#]]4&]
Out[]=
{s[s][s][k][s],s[s][s][k][k],s[s][k][s][s],s[s[k]][s][s],s[s][k][s][k],s[s[k]][s][k],s[s][k][k][s],s[s[k]][k][s],s[s][k][k][k],s[s[k]][k][k]}
In[]:=
Grid[Transpose[#],FrameAll]&/@Partition[SKFixedPointEvolveList/@Select[AllCombinators[5],Length[SKFixedPointEvolveList[#]]4&],5]
Out[]=
,
s[s][s][k][s] | s[s][s][k][k] | s[s][k][s][s] | s[s[k]][s][s] | s[s][k][s][k] |
s[k][s[k]][s] | s[k][s[k]][k] | s[s][k[s]][s] | s[k][s][s[s]] | s[s][k[s]][k] |
k[s][s[k][s]] | k[k][s[k][k]] | s[s][k[s][s]] | k[s[s]][s[s[s]]] | s[k][k[s][k]] |
s | k | s[s][s] | s[s] | s[k][s] |
s[s[k]][s][k] | s[s][k][k][s] | s[s[k]][k][s] | s[s][k][k][k] | s[s[k]][k][k] |
s[k][k][s[k]] | s[k][k[k]][s] | s[k][s][k[s]] | s[k][k[k]][k] | s[k][k][k[k]] |
k[s[k]][k[s[k]]] | k[s][k[k][s]] | k[k[s]][s[k[s]]] | k[k][k[k][k]] | k[k[k]][k[k[k]]] |
s[k] | s | k[s] | k | k[k] |
In[]:=
Histogram[%,{1}]
Out[]=
In[]:=
Histogram[Length/@SKFixedPointEvolveList/@AllCombinators[6],{1},FrameTrue]
Out[]=
In[]:=
Select[AllCombinators[6],Length[SKFixedPointEvolveList[#]]7&]
Out[]=
{s[s[s]][s][k][s],s[s[s]][s][k][k]}
In[]:=
Grid[Transpose[SKFixedPointEvolveList/@Select[AllCombinators[6],Length[SKFixedPointEvolveList[#]]7&]],FrameAll]
Out[]=
s[s[s]][s][k][s] | s[s[s]][s][k][k] |
s[s][k][s[k]][s] | s[s][k][s[k]][k] |
s[s[k]][k[s[k]]][s] | s[s[k]][k[s[k]]][k] |
s[k][s][k[s[k]][s]] | s[k][k][k[s[k]][k]] |
k[k[s[k]][s]][s[k[s[k]][s]]] | k[k[s[k]][k]][k[k[s[k]][k]]] |
k[s[k]][s] | k[s[k]][k] |
s[k] | s[k] |
In[]:=
Counts[LeafCount[SKFixedPointEvolve[#]]&/@AllCombinators[6]]
Out[]=
6606,738,104,96,828,2480,1380,512,4726,3408
In[]:=
Select[AllCombinators[6],LeafCount[SKFixedPointEvolve[#]]10&]
Out[]=
{s[s[s]][s][s][s],s[s][s][s[s]][s],s[s[s]][s][s][k],s[s][s][s[s]][k]}
In[]:=
Magnify[Grid[Transpose[PadRight[SKFixedPointEvolveList/@Select[AllCombinators[6],LeafCount[SKFixedPointEvolve[#]]10&],{Automatic,Automatic},""]],FrameAll],.7]
Out[]=
s[s[s]][s][s][s] | s[s][s][s[s]][s] | s[s[s]][s][s][k] | s[s][s][s[s]][k] |
s[s][s][s[s]][s] | s[s[s]][s[s[s]]][s] | s[s][s][s[s]][k] | s[s[s]][s[s[s]]][k] |
s[s[s]][s[s[s]]][s] | s[s][s][s[s[s]][s]] | s[s[s]][s[s[s]]][k] | s[s][k][s[s[s]][k]] |
s[s][s][s[s[s]][s]] | s[s[s[s]][s]][s[s[s[s]][s]]] | s[s][k][s[s[s]][k]] | s[s[s[s]][k]][k[s[s[s]][k]]] |
s[s[s[s]][s]][s[s[s[s]][s]]] | s[s[s[s]][k]][k[s[s[s]][k]]] |
In[]:=
SKFixedPointEvolveList/@Select[AllCombinators[6],LeafCount[SKFixedPointEvolve[#]]10&]
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][k],s[s][s][s[s]][k],s[s[s]][s[s[s]]][k],s[s][k][s[s[s]][k]],s[s[s[s]][k]][k[s[s[s]][k]]]},{s[s][s][s[s]][k],s[s[s]][s[s[s]]][k],s[s][k][s[s[s]][k]],s[s[s[s]][k]][k[s[s[s]][k]]]}}
In[]:=
Length/@%
Out[]=
{5,4,5,4}
In[]:=
Histogram[LeafCount[SKFixedPointEvolve[#]]&/@AllCombinators[6],{1},FrameTrue]
Out[]=
In[]:=
Select[AllCombinators[6],LeafCount[SKFixedPointEvolve[#]]5&]
Out[]=
{s[s[s[s]]][k][s],s[s[s]][s][k[s]],s[s[s[s]]][k][k],s[s[s]][s][k[k]],s[s[s]][k][s][s],s[s][s][k[s]][s],s[s[s]][k][s][k],s[s][s][k[s]][k],s[s][s][k[k]][s],s[s[s]][k][k[s]],s[s][s][k[k]][k],s[s[s]][k][k[k]]}
In[]:=
Length[Select[AllCombinators[6],LeafCount[SKFixedPointEvolve[#]]5&]]
Out[]=
12
In[]:=
Length[AllCombinators[6]]
Out[]=
2688
In[]:=
12/2688//N
Out[]=
0.00446429
In[]:=
PercentForm[%]
Check with other evolution
Check with other evolution
This finds the fixed point:
Checking
Checking
Newer code
Newer code
Size 8
Size 8
Size 7 check
Size 7 check
Size 8
Size 8
Rapid growth:
NOTE: big8 has 71; based on length 50, 76 survived
NOTE: big8 has 71; based on length 50, 76 survived
https://www.wolframscience.com/nks/p102--symbolic-systems/
[[[ Table of minimal conversions for blog ]]]
[[[ Table of minimal conversions for blog ]]]
All by-50-non-terminators
All by-50-non-terminators
[ see Combinators-18 ]
[ see Combinators-18 ]