In[]:=
Table[VertexCount[MultiwayTuringMachine[AllDeltaTMRules[{2,2}],{{1,t+1,0},Table[0,2t+1]},t,"StatesGraphStructure"]],{t,6}]
Out[]=
{9,36,100,248,576,1280}
In[]:=
ParallelTable[VertexCount[MultiwayTuringMachine[AllDeltaTMRules[{2,2}],{{1,t+1,0},Table[0,2t+1]},t,"StatesGraphStructure"]],{t,7}]
Out[]=
{9,36,100,248,576,1280,2768}
In[]:=
Ratios[%205]//N
Out[]=
{4.,2.77778,2.48,2.32258,2.22222}
In[]:=
Differences[%]
Out[]=
{27,64,148,328,704}
In[]:=
ParallelTable[VertexCount[MultiwayTuringMachine[AllDeltaTMRules[{2,2}],{{1,t+1,0},Table[0,2t+1]},t,"StatesGraphStructure"]],{t,0,3}]
Out[]=
{1,9,36,100}
In[]:=
ParallelTable[VertexCount[Graph[Flatten@Table[DirectedEdge@@@Partition[TuringMachine[tm,{{1,t+1,0},Table[0,2t+1]},t],2,1],{tm,0,4095}]]],{t,0,15}]
Out[]=
{0,9,36,68,94,144,248,322,382,458,559,659,737,823,921,1007}
In[]:=
Differences[%214]
Out[]=
{9,27,32,26,50,104,74,60,76,101,100,78,86,98,86}
In[]:=
ListLinePlot[%]
Out[]=
In[]:=
FindLinearRecurrence[{9,36,100,248,576,1280,2768}]
Out[]=
FindLinearRecurrence[{9,36,100,248,576,1280,2768}]
In[]:=
ParallelTable[If[t0,1,VertexCount[Graph[Flatten@Table[DirectedEdge@@@Partition[TuringMachine[tm,{{1,t+1,0},Table[0,2t+1]},t],2,1],{tm,0,4095}]]]],{t,0,100}]
Out[]=
{1,9,36,68,94,144,248,322,382,458,559,659,737,823,921,1007,1091,1189,1303,1399,1483,1575,1689,1793,1870,1950,2050,2146,2234,2340,2456,2550,2638,2730,2840,2948,3036,3128,3238,3332,3417,3515,3629,3727,3807,3901,4017,4123,4205,4289,4395,4493,4583,4689,4799,4889,4969,5055,5165,5275,5368,5460,5568,5658,5738,5838,5954,6052,6134,6228,6346,6454,6546,6638,6746,6846,6934,7040,7156,7250,7330,7416,7526,7638,7725,7817,7927,8017,8103,8205,8321,8419,8507,8605,8717,8823,8913,9001,9105,9199,9285}
In[]:=
ListLinePlot[%]
Out[]=
In[]:=
Differences[%218]
Out[]=
{8,27,32,26,50,104,74,60,76,101,100,78,86,98,86,84,98,114,96,84,92,114,104,77,80,100,96,88,106,116,94,88,92,110,108,88,92,110,94,85,98,114,98,80,94,116,106,82,84,106,98,90,106,110,90,80,86,110,110,93,92,108,90,80,100,116,98,82,94,118,108,92,92,108,100,88,106,116,94,80,86,110,112,87,92,110,90,86,102,116,98,88,98,112,106,90,88,104,94,86}
In[]:=
ListLinePlot[%]
Out[]=
In[]:=
With[{t=10},With[{rr=Table[DirectedEdge@@@Partition[TuringMachine[tm,{{1,t+1,0},Table[0,2t+1]},t],2,1],{tm,0,4095}]},Table[VertexCount[Graph[Flatten[Take[#,u]&/@rr]]],{u,t}]]]
Out[]=
{9,36,68,94,144,248,322,382,458,559}
In[]:=
With[{t=200},With[{rr=Table[DirectedEdge@@@Partition[TuringMachine[tm,{{1,t+1,0},Table[0,2t+1]},t],2,1],{tm,0,4095}]},Table[VertexCount[Graph[Flatten[Take[#,u]&/@rr]]],{u,t}]]]
Out[]=
In[]:=
Graph[With[{t=50},Flatten@ParallelTable[DirectedEdge@@@Partition[TuringMachine[tm,{{1,t+1,0},Table[0,2t+1]},t],2,1],{tm,0,4095}]]];
In[]:=
First[Values[ResourceFunction["GraphNeighborhoodVolumes"][%,{With[{t=50},{{1,t+1,0},Table[0,2t+1]}]}]]]
Out[]=
{1,9,36,92,180,290,436,596,765,943,1125,1301,1473,1637,1805,1963,2116,2260,2400,2518,2634,2734,2838,2932,3026,3112,3204,3264,3323,3377,3431,3483,3535,3587,3639,3689,3739,3789,3841,3891,3941,3991,4043,4091,4139,4187,4237,4279,4321,4357,4395}
In[]:=
Differences[%]
Out[]=
{8,27,56,88,110,146,160,169,178,182,176,172,164,168,158,153,144,140,118,116,100,104,94,94,86,92,60,59,54,54,52,52,52,52,50,50,50,52,50,50,50,52,48,48,48,50,42,42,36,38}
In[]:=
Graph[With[{t=100},Flatten@ParallelTable[DirectedEdge@@@Partition[TuringMachine[tm,{{1,t+1,0},Table[0,2t+1]},t],2,1],{tm,0,4095}]]];
In[]:=
First[Values[ResourceFunction["GraphNeighborhoodVolumes"][%,{With[{t=100},{{1,t+1,0},Table[0,2t+1]}]}]]]
Out[]=
{1,9,36,92,180,290,438,604,781,977,1175,1375,1573,1763,1953,2139,2326,2512,2698,2874,3050,3220,3390,3552,3716,3874,4032,4182,4331,4475,4621,4757,4895,5029,5167,5291,5413,5517,5623,5717,5817,5913,6008,6096,6188,6278,6372,6460,6552,6640,6732,6808,6872,6926,6982,7036,7090,7146,7201,7253,7305,7359,7413,7465,7517,7569,7621,7671,7721,7771,7823,7873,7923,7973,8025,8075,8125,8175,8227,8277,8327,8377,8429,8479,8529,8579,8631,8681,8731,8781,8833,8883,8933,8981,9031,9079,9127,9169,9213,9249,9285}
In[]:=
Differences[%]
Out[]=
{8,27,56,88,110,148,166,177,196,198,200,198,190,190,186,187,186,186,176,176,170,170,162,164,158,158,150,149,144,146,136,138,134,138,124,122,104,106,94,100,96,95,88,92,90,94,88,92,88,92,76,64,54,56,54,54,56,55,52,52,54,54,52,52,52,52,50,50,50,52,50,50,50,52,50,50,50,52,50,50,50,52,50,50,50,52,50,50,50,52,50,50,48,50,48,48,42,44,36,36}
In[]:=
ListLinePlot[{%242,%245}]
Out[]=
Finding “explorer” machines
Finding “explorer” machines
Identifying spokes
Identifying spokes