wme=WolframModel[{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}},{{0,0},{0,0}},10]
In[]:=
Out[]=
Graph[Rule@@@#]&/@%["StatesList"]
In[]:=
Out[]=
Graph[Rule@@@#,GraphLayout"SpringElectricalEmbedding",VertexLabelsAutomatic]&/@Take[wme["StatesList"],6]
In[]:=
Out[]=
Quit
In[]:=
VertexList

In[]:=
Out[]=
VertexCount

In[]:=
483
Out[]=
EdgeCount

In[]:=
966
Out[]=
VertexOutDegree

In[]:=
Out[]=
Histogram[%]
In[]:=
Out[]=
MatrixPlotAdjacencyMatrix

In[]:=
Out[]=
NeighborhoodGraph
,100
In[]:=
Out[]=
Graph[Rule@@@wme[2],GraphLayout"LinearEmbedding"]
In[]:=
Out[]=
Table[Graph[Rule@@@wme[i],GraphLayout"LinearEmbedding"],{i,5}]
In[]:=
Out[]=
Table[Graph[Rule@@@wme[i],GraphLayout"GravityEmbedding"],{i,5}]
In[]:=
Out[]=
Table[Graph[Rule@@@wme[i],GraphLayout"GravityEmbedding"],{i,10}]
In[]:=
Out[]=
Table[Graph[Rule@@@wme[i],GraphLayout"HighDimensionalEmbedding"],{i,10}]
In[]:=
Out[]=
Table[Graph3D[Rule@@@wme[i],GraphLayout"GravityEmbedding"],{i,10}]
In[]:=
Out[]=
Graph[Rule@@@WolframModel[{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}},{{0,0},{0,0}},13,"FinalState"]]
In[]:=
Out[]=
Graph3D[%,GraphLayout"GravityEmbedding"]
In[]:=
Out[]=
GraphPlot3D[%29]
In[]:=
Out[]=
Show[%32,BoxedTrue,AxesTrue,FrameTicksAutomatic]
In[]:=
Out[]=
Show[%32,BoxedTrue,AxesTrue,FrameTicksAutomatic,PlotRange{0,2}]
In[]:=
Out[]=
UndirectedGraph[%28]
In[]:=
Out[]=
GraphNeigborhoodVolumes[%]
In[]:=
Out[]=
ListLinePlot[Values[%39]]
In[]:=
$Aborted[]
Out[]=
Values[%39];
In[]:=
Mean[Take[#,20]&/@%41]//N
In[]:=
{5.,14.8598,31.4798,56.7519,91.849,138.141,197.579,272.32,364.003,473.658,602.087,749.545,916.906,1103.5,1306.77,1522.8,1744.48,1963.66,2173.9,2369.26}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
ListLogPlot[%46,JoinedTrue]
In[]:=
Out[]=
Differences[%46]
In[]:=
{9.85982,16.6199,25.2721,35.0971,46.2922,59.438,74.741,91.6828,109.655,128.428,147.458,167.361,186.59,203.269,216.039,221.675,219.185,210.232,195.364}
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
ListLogLogPlot[%46]
In[]:=
Out[]=
FindFit[%46,r^d,d,r]
In[]:=
{d2.62004}
Out[]=
MeanAround/@Transpose[Take[#,20]&/@%41]//N
In[]:=
{5.000±0.028,14.86±0.08,31.48±0.18,56.75±0.34,91.8±0.6,138.1±0.8,197.6±1.2,272.3±1.6,364.0±2.1,473.7±2.7,602.1±3.3,750.±4.,917.±5.,1103.±6.,1307.±6.,1523.±7.,1744.±7.,1964.±8.,2174.±7.,2369.±7.}
Out[]=
ListLogLogPlot[%]
In[]:=
Out[]=
Length[{4,10,23,51,98,170,277,425,653,928,1238,1519,1767,1987,2185,2421,2634,2833,2942,3010,3031,3039,3039}]
In[]:=
23
Out[]=
Counts[Length/@%41]
In[]:=
2396,2231,27452,28447,24139,26301,25209,30410,29508,31246,214,3356,32140
Out[]=
BarChart[%]
In[]:=
Out[]=

Larger run

Graph[Rule@@@WolframModel[{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}},{{0,0},{0,0}},16,"FinalState"]]
In[]:=
Out[]=
GraphPlot[%]
In[]:=
Out[]=
MeanAround/@Transpose[Take[#,30]&/@GraphNeigborhoodVolumes[UndirectedGraph[%75]]]//N
In[]:=
Transpose
:The first two levels of 613{4,9,16,32,82,175,268,420,609,814,1057,1317,1653,2082,2634,3248,3934,4679,5426,6153,6913,7680,8575,9439,10316,11187,12059,12851,13655,14425},5616{5,11,23,57,132,224,346,510,713,925,1187,1485,1869,2371,2953,3640,4373,5145,5904,6645,7415,8291,9181,10060,10921,11808,12630,13452,14262,15038},19005,19007{4,12,22,38,71,104,136,187,244,283,337,418,515,667,854,1049,1237,1411,1597,1842,2111,2419,2732,3058,3366,3667,3994,4382,4803,5247} cannot be transposed.
Out[]=
%78[[1,1]];
In[]:=
Head[%]
In[]:=
Association
Out[]=
Min[Length/@Values[%80]]
In[]:=
30
Out[]=
MeanAround/@Transpose[Take[#,25]&/@Values[%80]]
In[]:=
Out[]=
ListLogLogPlot[%]
In[]:=
Out[]=
First/@%86
In[]:=
{5.,14.8444,31.3474,56.6893,92.5,140.314,201.459,277.383,369.542,478.858,605.747,751.505,918.495,1109.31,1326.37,1571.91,1846.96,2151.8,2485.76,2849.69,3244.71,3672.17,4132.37,4625.59,5152.18}
Out[]=
FindFit[%,r^d,d,r]
In[]:=
{d2.65558}
Out[]=
FindFit[%90,ar^d,{d,a},r]
In[]:=
{d2.63655,a1.0605}
Out[]=
Table[n^2.66,{n,20}]
In[]:=
{1.,6.32033,18.5841,39.9466,72.3203,117.458,176.995,252.476,345.37,457.088,588.985,742.373,918.521,1118.67,1344.01,1595.73,1874.97,2182.85,2520.49,2888.95}
Out[]=
ListLogLogPlot[{%86,%}]
In[]:=
Out[]=

Local Neighborhoods

state13=Graph[Rule@@@WolframModel[{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}},{{0,0},{0,0}},13,"FinalState"]];
In[]:=
Table[HighlightGraph[Subgraph[state13,VertexOutComponent[state13,i,2],GraphLayout"SpringElectricalEmbedding"],i],{i,30}]
In[]:=
Out[]=
Table[Table[Length[VertexOutComponent[state13,i,k]],{k,0,8}],{i,30}]
In[]:=
Out[]=
ListLinePlot[%]
In[]:=
Out[]=
Table[Table[Length[VertexOutComponent[state13,i,k]],{k,0,8}],{i,1000,1050}];
In[]:=
ListLinePlot[%]
In[]:=
Out[]=
ListLinePlot[Table[Table[Length[VertexOutComponent[state13,i,k]],{k,0,8}],{i,RandomInteger[{1,VertexCount[state13]},100]}],PlotRangeAll]
In[]:=
Out[]=
GraphNeigborhoodVolumes[Graph[Rule@@@wme["FinalState"]]]
In[]:=
Out[]=

Change Indication

WolfraModelDifferenceEvolution[{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}},{{0,0},{0,0}},3,3]
In[]:=
Out[]=
WolfraModelDifferenceEvolution[{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}},{{0,0},{0,0}},5,5]
In[]:=
Out[]=
WolfraModelDifferenceEvolution[{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}},{{0,0},{0,0}},7,3]
In[]:=
Out[]=
Graph[Rule@@@#,GraphLayout"SpringElectricalEmbedding"]&/@WolframModel[{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}},{{0,0},{0,0}},8,"StatesList"]
In[]:=
Out[]=
HighlightGraphChanges[%]
In[]:=
Out[]=

Multiway version

MultiwaySystem["WolframModel"{{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}}},{{{0,0},{0,0}}},3,"StatesGraph",VertexSize1]
In[]:=
Out[]=
MultiwaySystem["WolframModel"{{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}}},{{{0,0},{0,0}}},3,"StatesGraph",VertexSize1]
In[]:=
Out[]=
MultiwaySystem["WolframModel"{{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}}},{{{0,0},{0,0}}},4,"StatesGraph",VertexSize1]
In[]:=
Out[]=
MultiwaySystem["WolframModel"{{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}}},{{{0,0},{0,0}}},5,"StatesGraph",VertexSize1]
In[]:=
Out[]=
MultiwaySystem["WolframModel"{{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}}},{{{0,0},{0,0}}},4,"AllEventsList"]
In[]:=
Replace
:{v1_,v2_} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.
Replace
:{v1_,v3_} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.
{{{Null{{0,0},{0,0}},Null,{{},{}}}},{{{{v1_,v2_},{v1_,v3_}},{{0,0},{0,0}},{{},{}}}},{},{},{}}
Out[]=
InputForm[%]
In[]:=
Graph[{{{0, 0}, {0, 0}}, {{{v1_, v2_}, {v1_, v3_}}, {{0, 0}, {0, 0}}, {{}, {}}}, {{0, 0}, {0, v4$157975}, {0, v4$157975},
{0, v4$157975}}, {{0, 0}, {0, v4$157975}, {0, v4$157975}, {0, v4$157990}, {0, v4$157990}, {v4$157975, v4$157990}},
{{0, 0}, {0, v4$157975}, {0, v4$158047}, {v4$157975, v4$157990}, {v4$157975, v4$158047}, {v4$157990, v4$158047}},
{{0, 0}, {0, v4$157975}, {0, v4$157990}, {0, v4$157990}, {0, v4$158040}, {0, v4$158040}, {v4$157975, v4$157990},
{v4$157975, v4$158040}}, {Replace[{{0, 0}, {0, 0}}, {v1_, v2_}], Replace[{{0, 0}, {0, 0}}, {v1_, v3_}]}},
{DirectedEdge[{{0, 0}, {0, 0}}, {{{v1_, v2_}, {v1_, v3_}}, {{0, 0}, {0, 0}}, {{}, {}}}],
DirectedEdge[{{{v1_, v2_}, {v1_, v3_}}, {{0, 0}, {0, 0}}, {{}, {}}}, {Replace[{{0, 0}, {0, 0}}, {v1_, v2_}],
Replace[{{0, 0}, {0, 0}}, {v1_, v3_}]}]}, {PerformanceGoal -> Quality,
VertexShapeFunction -> {{{0, 0}, {0, 0}} -> (WolframModelStateRendering[#1, #2, #3] & ),
{{0, 0}, {0, v4$157975}, {0, v4$158047}, {v4$157975, v4$157990}, {v4$157975, v4$158047}, {v4$157990, v4$158047}} ->
(WolframModelStateRendering[#1, #2, #3] & ), {{0, 0}, {0, v4$157975}, {0, v4$157975}, {0, v4$157975}} ->
(WolframModelStateRendering[#1, #2, #3] & ), {{0, 0}, {0, v4$157975}, {0, v4$157975}, {0, v4$157990}, {0, v4$157990},
{v4$157975, v4$157990}} -> (WolframModelStateRendering[#1, #2, #3] & ),
{{0, 0}, {0, v4$157975}, {0, v4$157990}, {0, v4$157990}, {0, v4$158040}, {0, v4$158040}, {v4$157975, v4$157990},
{v4$157975, v4$158040}} -> (WolframModelStateRendering[#1, #2, #3] & ), {{{v1_, v2_}, {v1_, v3_}}, {{0, 0}, {0, 0}}, {{}, {}}} ->
Diamond}, VertexSize -> {1}}]
Out[]//InputForm=
StringeventDecompositionFunction
MultiwaySystem["WolframModel"{{{1,2},{1,3}}{{1,3},{1,4},{2,4},{3,4}}}"Sequential",{{{0,0},{0,0}}},5,"StatesGraph",VertexSize1]
In[]:=
Replace
:{v1_,v2_} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.
Replace
:{v1_,v3_} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.
Replace
:{v1_,v2_} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.
General
:Further output of Replace::reps will be suppressed during this calculation.
Out[]=

Causal graph

wme
In[]:=
Out[]=
%["CausalGraph"]
In[]:=
Out[]=
Not causal invariant