11{1,1,1,1,1}
In[]:=
OneSidedTuringMachineEvolution[makeTM[5{1,1,1,1,1}],1,20][[All,1,1]]
Out[]=
{1,3,6,12,20,28,36,44}
In[]:=
OneSidedTuringMachineEvolution[makeTM[5{1,1,1,1,1}],2,20][[All,1,1]]
Out[]=
{1,2,5,10,18,26,34,42}
In[]:=
OneSidedTuringMachineEvolution[makeTM[5{1,1,1,1,1}],3,20][[All,1,1]]
Out[]=
{1,3,7,14,22,30,38,46}
In[]:=
makeTM[5{1,1,1,1,1}]
Out[]=
{{1,0}{2,0,-1},{1,1}{3,0,-1},{2,0}{4,0,-1},{2,1}{5,0,-1},{3,0}{6,0,-1},{3,1}{7,0,-1},{4,0}{8,0,-1},{4,1}{9,0,-1},{5,0}{10,0,-1},{5,1}{11,0,-1},{6,0}{12,0,-1},{6,1}{13,0,-1},{7,0}{14,0,-1},{7,1}{15,0,-1},{12,0}{20,0,1},{20,0}{28,1,1},{28,0}{36,0,1},{36,0}{44,1,1},{10,0}{18,0,1},{18,0}{26,1,1},{26,0}{34,0,1},{34,0}{42,1,1},{14,0}{22,0,1},{22,0}{30,1,1},{30,0}{38,0,1},{38,0}{46,1,1},{9,0}{17,0,1},{17,0}{25,1,1},{25,0}{33,0,1},{33,0}{41,1,1},{13,0}{21,0,1},{21,0}{29,1,1},{29,0}{37,0,1},{37,0}{45,1,1}}
In[]:=
Graph[#[[1,1]]->#[[2,1]]&/@makeTM[5{1,1,1,1,1}],VertexLabels->Automatic]
Out[]=
In[]:=
Graph[#[[1,1]]->#[[2,1]]&/@makeTM[{1,1,1,1,1}],VertexLabels->Automatic]
Out[]=
In[]:=
Graph[#[[1,1]]->#[[2,1]]&/@makeTM[{1,2,3,2,1}],VertexLabels->Automatic]
Out[]=
In[]:=
Graph[#[[1,1]]->#[[2,1]]&/@makeTM[32{1,1,1}],VertexLabels->Automatic]
Out[]=
In[]:=
Graph[#[[1,1]]->#[[2,1]]&/@makeTM[0{1,1,1}],VertexLabels->Automatic]
Out[]=
l
Non-Halting
Non-Halting
In[]:=
OneSidedTuringMachineFunction[{1227985,3,2},{1,400},200]
s=3, k=2
s=3, k=2
v2
v2
Gets too big
Gets too big
Gets infinite
Gets infinite
All these should be added to periodic
Gets big
Gets big
Intermediate Growth
Intermediate Growth
Exponential: linear on log scale
Power law: linear on log-log scale
Power law: linear on log-log scale
Recognizable Functions
Recognizable Functions
Closed Forms
Closed Forms
Out[]//InputForm=
{HoldForm[1], HoldForm[2*n + 1], HoldForm[2*n - 1], HoldForm[3], HoldForm[If[n == 1, 1, 3]], HoldForm[2*n + 3], HoldForm[4*n - 1], HoldForm[If[n == 1, 1, 4*n - 5]], HoldForm[If[n == 1, 1, 2*n + 1]], HoldForm[If[n == 1, 3, 5]], HoldForm[If[n == 2, 3, 5]],
HoldForm[4*n + 1], HoldForm[If[EvenQ[n], 2*n + 3, 2*n - 1]], HoldForm[If[EvenQ[n], 2*n - 1, 2*n + 3]], HoldForm[4*n + 3], HoldForm[4*n - 3], HoldForm[If[n == 1, 1, 5]], HoldForm[If[n <= 3, 2*n - 1, 5]], HoldForm[If[n == 1, 1, 4*n - 1]],
HoldForm[(1/2)*((-1)^(n + 1) + 3 + 6*n)], HoldForm[If[n == 1, 1, 2*n + 3]], HoldForm[If[n == 1, 1, 4*n + 3]], HoldForm[(-1)^(n + 1) + 2 + 2*n], HoldForm[If[EvenQ[n], 3*n - 1, 3*n - 2]], HoldForm[4*n + 5], HoldForm[6*n - 1], HoldForm[2^(2 + n) - 3],
HoldForm[If[n <= 2, 4*n + 3, 6*n - 3]], HoldForm[If[n == 1, 1, 4*Floor[n/2] + 3]], HoldForm[If[EvenQ[n], 3*n + 3, 3*n - 2]], HoldForm[If[EvenQ[n], 2*n + 5, 2*n - 1]], HoldForm[2*n^2 + 4*n + 1], HoldForm[If[EvenQ[n], 3*n - 3, 3*n - 2]],
HoldForm[If[EvenQ[n], 3*n + 1, 3*n]], HoldForm[If[EvenQ[n], 3*n - 3, 3*n + 4]], HoldForm[If[EvenQ[n], 2*n + 3, 2*n + 1]], HoldForm[If[EvenQ[n], 3*n - 1, 3*n + 4]], HoldForm[If[EvenQ[n], 3*n + 5, 3*n - 2]], HoldForm[If[EvenQ[n], 2*n - 1, 2*n + 5]],
HoldForm[2^(1 + n) - 3], HoldForm[2*n + 5], HoldForm[If[n == 1, 9, 4*n + 3]], HoldForm[If[n == 1, 1, If[EvenQ[n], 4*n + 3, 4*n - 5]]], HoldForm[2^n - 1], HoldForm[6*n + 3], HoldForm[8*n - 3], HoldForm[2*n^2 + 6*n + 3], HoldForm[2*n^2 + 2*n + 1],
HoldForm[2*n^2 + 8*n + 7], HoldForm[If[EvenQ[n], 8*n + 1, 8*n - 1]], HoldForm[If[n == 1, 1, 2^(n + 1) - 1]], HoldForm[If[n == 1, 3, 10*n - 13]], HoldForm[2*n^2 + 2*n - 1], Unknown, HoldForm[2^(1 + n) - 1], HoldForm[If[n == 1, 3, 6*n - 5]], Unknown,
HoldForm[If[n == 1, 3, 2*n + 3]], HoldForm[If[n == 1, 3, 4*n + 3]], HoldForm[2*n^2 - 2*n + 1], HoldForm[If[n <= 2, 4*n - 3, 4*n - 1]], HoldForm[If[n == 1, 1, If[EvenQ[n], 3*n + 5, 3*n]]], HoldForm[If[n == 1, 5, 8*n - 9]], HoldForm[If[n == 1, 5, 6*n - 5]],
HoldForm[If[EvenQ[n], 4*n - 5, 4*n + 3]], HoldForm[If[n == 1, 9, If[n == 2, 7, If[EvenQ[n], 2*n + 5, 2*n + 9]]]], HoldForm[If[EvenQ[n], (1/2)*(n^2 + 4*n + 10), (1/2)*(n^2 + 10*n + 15)]], HoldForm[If[n == 1, 1, 6*n - 7]], HoldForm[2*n^2 - 1],
HoldForm[If[n <= 2, 2*n - 1, 6*n - 11]], HoldForm[If[n == 1, 1, If[EvenQ[n], 3*n + 7, 3*n]]]}
HoldForm[4*n + 1], HoldForm[If[EvenQ[n], 2*n + 3, 2*n - 1]], HoldForm[If[EvenQ[n], 2*n - 1, 2*n + 3]], HoldForm[4*n + 3], HoldForm[4*n - 3], HoldForm[If[n == 1, 1, 5]], HoldForm[If[n <= 3, 2*n - 1, 5]], HoldForm[If[n == 1, 1, 4*n - 1]],
HoldForm[(1/2)*((-1)^(n + 1) + 3 + 6*n)], HoldForm[If[n == 1, 1, 2*n + 3]], HoldForm[If[n == 1, 1, 4*n + 3]], HoldForm[(-1)^(n + 1) + 2 + 2*n], HoldForm[If[EvenQ[n], 3*n - 1, 3*n - 2]], HoldForm[4*n + 5], HoldForm[6*n - 1], HoldForm[2^(2 + n) - 3],
HoldForm[If[n <= 2, 4*n + 3, 6*n - 3]], HoldForm[If[n == 1, 1, 4*Floor[n/2] + 3]], HoldForm[If[EvenQ[n], 3*n + 3, 3*n - 2]], HoldForm[If[EvenQ[n], 2*n + 5, 2*n - 1]], HoldForm[2*n^2 + 4*n + 1], HoldForm[If[EvenQ[n], 3*n - 3, 3*n - 2]],
HoldForm[If[EvenQ[n], 3*n + 1, 3*n]], HoldForm[If[EvenQ[n], 3*n - 3, 3*n + 4]], HoldForm[If[EvenQ[n], 2*n + 3, 2*n + 1]], HoldForm[If[EvenQ[n], 3*n - 1, 3*n + 4]], HoldForm[If[EvenQ[n], 3*n + 5, 3*n - 2]], HoldForm[If[EvenQ[n], 2*n - 1, 2*n + 5]],
HoldForm[2^(1 + n) - 3], HoldForm[2*n + 5], HoldForm[If[n == 1, 9, 4*n + 3]], HoldForm[If[n == 1, 1, If[EvenQ[n], 4*n + 3, 4*n - 5]]], HoldForm[2^n - 1], HoldForm[6*n + 3], HoldForm[8*n - 3], HoldForm[2*n^2 + 6*n + 3], HoldForm[2*n^2 + 2*n + 1],
HoldForm[2*n^2 + 8*n + 7], HoldForm[If[EvenQ[n], 8*n + 1, 8*n - 1]], HoldForm[If[n == 1, 1, 2^(n + 1) - 1]], HoldForm[If[n == 1, 3, 10*n - 13]], HoldForm[2*n^2 + 2*n - 1], Unknown, HoldForm[2^(1 + n) - 1], HoldForm[If[n == 1, 3, 6*n - 5]], Unknown,
HoldForm[If[n == 1, 3, 2*n + 3]], HoldForm[If[n == 1, 3, 4*n + 3]], HoldForm[2*n^2 - 2*n + 1], HoldForm[If[n <= 2, 4*n - 3, 4*n - 1]], HoldForm[If[n == 1, 1, If[EvenQ[n], 3*n + 5, 3*n]]], HoldForm[If[n == 1, 5, 8*n - 9]], HoldForm[If[n == 1, 5, 6*n - 5]],
HoldForm[If[EvenQ[n], 4*n - 5, 4*n + 3]], HoldForm[If[n == 1, 9, If[n == 2, 7, If[EvenQ[n], 2*n + 5, 2*n + 9]]]], HoldForm[If[EvenQ[n], (1/2)*(n^2 + 4*n + 10), (1/2)*(n^2 + 10*n + 15)]], HoldForm[If[n == 1, 1, 6*n - 7]], HoldForm[2*n^2 - 1],
HoldForm[If[n <= 2, 2*n - 1, 6*n - 11]], HoldForm[If[n == 1, 1, If[EvenQ[n], 3*n + 7, 3*n]]]}
Grouped by function
Grouped by function