ResourceFunction["MultiwaySystem"][{"BA""AB"},{"BBAAA"},12,"EvolutionEventsGraph"]
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TransitiveClosureGraph[%]
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Transitive Percolation

Range[10]
In[]:=
{1,2,3,4,5,6,7,8,9,10}
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RandomVariate[PoissonDistribution[10]]
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12
Out[]=
{u,v}
Table[RandomReal[{0,1},2],12]
In[]:=
{{0.495492,0.320783},{0.557509,0.455764},{0.311316,0.699236},{0.850816,0.636443},{0.588183,0.900362},{0.527344,0.201527},{0.704206,0.256578},{0.350039,0.656963},{0.241395,0.0868937},{0.703093,0.753115},{0.410354,0.0337528},{0.502144,0.728207}}
Out[]=
Graphics[Point[RotationMatrix[45Degree].#&/@Sort[Table[RandomReal[{0,1},2],50],Function[{p,q},p[[1]]<q[[1]]&&p[[2]]<q[[2]]]]]]
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Out[]=
Outer[Function[{p,q},p[[1]]<q[[1]]&&p[[2]]<q[[2]]],#,#,1]&[Table[RandomReal[{0,1},2],20]]
ListLinePlot[%]
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​
RandomGraph[{50,70}]
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growthStep[graph_,probability_]:=With[{newVertex=Max[VertexList[graph],0]+1},Graph[Append[VertexList[graph],newVertex],Join[EdgeList[graph],If[RandomReal[]<probability,#newVertex,Nothing]&/@VertexList[graph]]]]
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Framed/@NestList[growthStep[#,.2]&,Graph[{12}],10]
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Out[]=
NestList[growthStep[#,.2]&,Graph[{12}],10]
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TransitiveReductionGraph/@%
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Out[]=
Table[TransitiveReductionGraph[Nest[growthStep[#,.2]&,Graph[{12}],20]],10]
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Out[]=
Table[TransitiveReductionGraph[Nest[growthStep[#,.7]&,Graph[{12}],50]],5]
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Out[]=
Table[TransitiveReductionGraph[Nest[growthStep[#,.2]&,Graph[{12}],50]],5]
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Out[]=
Table[TransitiveReductionGraph[Nest[growthStep[#,.5]&,Graph[{12}],50]],5]
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Out[]=
Table[LayeredGraphPlot[TransitiveReductionGraph[Nest[growthStep[#,.5]&,Graph[{12}],50]]],5]
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Out[]=
Table[Graph[TransitiveReductionGraph[Nest[growthStep[#,.2]&,Graph[{12}],50]],GraphLayout"LayeredDigraphEmbedding"],5]
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Out[]=
FutureLightCone[g_,i_,t_Integer]:=HighlightGraph[g,Subgraph[g,VertexOutComponent[g,i,t]]]
In[]:=
FutureLightCone
,1,2
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Out[]=
gg=Graph[TransitiveReductionGraph[Nest[growthStep[#,.1]&,Graph[{12}],200]],GraphLayout"LayeredDigraphEmbedding"]
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Midpoint scaling dimension

FutureLightCone[gg,
RandomSubset[list_]:=With[{n=Length[list]},Pick[list,IntegerDigits[RandomInteger[2^n],2,n],1]];
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CausalPercolation[g_]:=Module[{n},n=VertexCount[g]+1;​​EdgeAdd[g,RandomSubset[Thread[Range[n-1]n]]]]
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TransitiveReductionGraph/@NestList[CausalPercolation,Graph[{12}],10]
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