Checking 1,2

In[]:=
OneSidedTuringMachineFunction[{m,1,2},{1,20},200]
In[]:=
OneSidedTuringMachineFunction[{All,1,2},{1,20},200,"Value"]
Out[]=
{{Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined},{0,2,0,4,4,6,0,8,8,10,8,12,12,14,0,16,16,18,16,20},{Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined},{3,3,7,5,7,7,15,9,11,11,15,13,15,15,31,17,19,19,23,21},{0,Undefined,2,Undefined,4,Undefined,6,Undefined,8,Undefined,10,Undefined,12,Undefined,14,Undefined,16,Undefined,18,Undefined},{0,2,2,4,4,6,6,8,8,10,10,12,12,14,14,16,16,18,18,20},{0,0,2,0,4,4,6,0,8,8,10,8,12,12,14,0,16,16,18,16},{0,3,2,5,4,7,6,9,8,11,10,13,12,15,14,17,16,19,18,21},{Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined},{Undefined,2,Undefined,4,Undefined,6,Undefined,8,Undefined,10,Undefined,12,Undefined,14,Undefined,16,Undefined,18,Undefined,20},{Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined},{Undefined,3,Undefined,5,Undefined,7,Undefined,9,Undefined,11,Undefined,13,Undefined,15,Undefined,17,Undefined,19,Undefined,21},{1,Undefined,3,Undefined,5,Undefined,7,Undefined,9,Undefined,11,Undefined,13,Undefined,15,Undefined,17,Undefined,19,Undefined},{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20},{1,3,3,7,5,7,7,15,9,11,11,15,13,15,15,31,17,19,19,23},{1,3,3,5,5,7,7,9,9,11,11,13,13,15,15,17,17,19,19,21}}
In[]:=
OneSidedTuringMachineFunction[{All,1,2},{1,20},200,"Steps"]
Out[]=
{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{3,1,5,1,3,1,7,1,3,1,5,1,3,1,9,1,3,1,5,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{3,1,5,1,3,1,7,1,3,1,5,1,3,1,9,1,3,1,5,1},{1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},{1,3,1,5,1,3,1,7,1,3,1,5,1,3,1,9,1,3,1,5},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1},{1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},{1,3,1,5,1,3,1,7,1,3,1,5,1,3,1,9,1,3,1,5},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}}
In[]:=
GatherByTranspose
,
,First
Out[]=
{{{{Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined,Undefined},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}},{{{0,2,0,4,4,6,0,8,8,10,8,12,12,14,0,16,16,18,16,20},{3,1,5,1,3,1,7,1,3,1,5,1,3,1,9,1,3,1,5,1}}},{{{3,3,7,5,7,7,15,9,11,11,15,13,15,15,31,17,19,19,23,21},{3,1,5,1,3,1,7,1,3,1,5,1,3,1,9,1,3,1,5,1}}},{{{0,Undefined,2,Undefined,4,Undefined,6,Undefined,8,Undefined,10,Undefined,12,Undefined,14,Undefined,16,Undefined,18,Undefined},{1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0}}},{{{0,2,2,4,4,6,6,8,8,10,10,12,12,14,14,16,16,18,18,20},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}}},{{{0,0,2,0,4,4,6,0,8,8,10,8,12,12,14,0,16,16,18,16},{1,3,1,5,1,3,1,7,1,3,1,5,1,3,1,9,1,3,1,5}}},{{{0,3,2,5,4,7,6,9,8,11,10,13,12,15,14,17,16,19,18,21},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}}},{{{Undefined,2,Undefined,4,Undefined,6,Undefined,8,Undefined,10,Undefined,12,Undefined,14,Undefined,16,Undefined,18,Undefined,20},{0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1}}},{{{Undefined,3,Undefined,5,Undefined,7,Undefined,9,Undefined,11,Undefined,13,Undefined,15,Undefined,17,Undefined,19,Undefined,21},{0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1}}},{{{1,Undefined,3,Undefined,5,Undefined,7,Undefined,9,Undefined,11,Undefined,13,Undefined,15,Undefined,17,Undefined,19,Undefined},{1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0}}},{{{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}}},{{{1,3,3,7,5,7,7,15,9,11,11,15,13,15,15,31,17,19,19,23},{1,3,1,5,1,3,1,7,1,3,1,5,1,3,1,9,1,3,1,5}}},{{{1,3,3,5,5,7,7,9,9,11,11,13,13,15,15,17,17,19,19,21},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}}}}
In[]:=
Length/@%
Out[]=
{4,1,1,1,1,1,1,1,1,1,1,1,1}

Maximum Growth

TuringMachine[‸]
In[]:=
#[[1,3]]&/@OneSidedTuringMachineEvolution[{378,2,2},7,100]
Out[]=
{0,-1,-2,-3,-2,-3,-2,-1,-2,-3,-2,-3,-2,-1,0,-1,-2,-3,-2,-3,-2,-1,-2,-3,-2,-3,-2,-1,0,1}
In[]:=
ListStepPlot[%]
Out[]=
5
10
15
20
25
30
-3
-2
-1
1
In[]:=
{#[[1,3]],Take[Last[#],-5]}&/@OneSidedTuringMachineEvolution[{378,2,2},7,100]
Out[]=
{{0,{0,1,1,1,0}},{-1,{0,1,1,0,0}},{-2,{0,1,0,0,0}},{-3,{0,0,0,0,0}},{-2,{0,0,0,0,0}},{-3,{0,1,0,0,0}},{-2,{0,1,0,0,0}},{-1,{0,1,0,0,0}},{-2,{0,1,1,0,0}},{-3,{0,0,1,0,0}},{-2,{0,0,1,0,0}},{-3,{0,1,1,0,0}},{-2,{0,1,1,0,0}},{-1,{0,1,1,0,0}},{0,{0,1,1,0,0}},{-1,{0,1,1,1,0}},{-2,{0,1,0,1,0}},{-3,{0,0,0,1,0}},{-2,{0,0,0,1,0}},{-3,{0,1,0,1,0}},{-2,{0,1,0,1,0}},{-1,{0,1,0,1,0}},{-2,{0,1,1,1,0}},{-3,{0,0,1,1,0}},{-2,{0,0,1,1,0}},{-3,{0,1,1,1,0}},{-2,{0,1,1,1,0}},{-1,{0,1,1,1,0}},{0,{0,1,1,1,0}},{1,{0,1,1,1,0}}}
In[]:=
Length[%]
Out[]=
30
In[]:=
Length[%]
Out[]=
30
In[]:=
ListStepPlot[Most[#[[1,3]]&/@OneSidedTuringMachineEvolution[{378,2,2},63,2^11]],AspectRatio->1/5,Frame->True,PlotStyle->Gray,FrameLabel->{"step","head offset"}]
Out[]=
In[]:=
Table[Max[OneSidedTuringMachineFunction[{924,2,2},{2^j,2^(j+1)-1},2^17]],{j,0,14}]
Out[]=
{0,2,6,14,30,62,126,254,510,1022,2046,4094,8190,16382,32766}
In[]:=
FindSequenceFunction[%294,n]
Out[]=
-2+
n
2
In[]:=
Expand[%]
Out[]=
{0,2,6,14,30,62,126,254,510,1022,2046,4094,8190,16382,32766}
In[]:=
dmach
Out[]=

⋯1⋯

Full expression not available
(
original memory size:
1.2 MB)
In[]:=
Length[dmach]
Out[]=
44
In[]:=
Take[dmach,2]
Out[]=
In[]:=
Length[{3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}]