{{3,2}}{{5,2}},4

Select[Union[Table[RandomWolframModelRule[{{3,2}}{{5,2}},4],50]],NewVerticesQ]
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ParallelMapMonitored[SafeHyperModelTestButton[#,10,4]&,%]
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WolframModel[{{1,1},{2,1},{3,3}}{{2,1},{2,2},{3,3},{4,1},{4,2}},Table[0,3,2],20]
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Graph[Rule@@@%["FinalState"]]
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Graph[Rule@@@WolframModel[{{1,1},{2,1},{3,3}}{{2,1},{2,2},{3,3},{4,1},{4,2}},Table[0,3,2],40,"FinalState"]]
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Another rule

RulePlot[WolframModel[{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}}]]
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RulePlot[WolframModel[{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}}],VertexLabelsAutomatic]
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WolframModel[{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}},Table[0,3,2],20]
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Graph[Rule@@@%["FinalState"]]
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WolframModel[{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}},Table[0,3,2],40]
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Graph[Rule@@@%["FinalState"]]
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Length/@%140["StatesList"]
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{3,5,7,9,13,17,21,25,29,35,41,47,55,63,73,83,95,109,123,139,157,177,201,227,257,289,327,367,413,465,521,587,659,741,831,935,1049,1179,1321,1485,1663}
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Differences[%]
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{2,2,2,4,4,4,4,4,6,6,6,8,8,10,10,12,14,14,16,18,20,24,26,30,32,38,40,46,52,56,66,72,82,90,104,114,130,142,164,178}
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Differences[%]
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{0,0,2,0,0,0,0,2,0,0,2,0,2,0,2,2,0,2,2,2,4,2,4,2,6,2,6,6,4,10,6,10,8,14,10,16,12,22,14}
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Ratios[%142]//N
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{1.66667,1.4,1.28571,1.44444,1.30769,1.23529,1.19048,1.16,1.2069,1.17143,1.14634,1.17021,1.14545,1.15873,1.13699,1.14458,1.14737,1.12844,1.13008,1.1295,1.12739,1.13559,1.12935,1.13216,1.12451,1.13149,1.12232,1.12534,1.12591,1.12043,1.12668,1.12266,1.12443,1.12146,1.12515,1.12193,1.12393,1.12044,1.12415,1.11987}
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ListLinePlot[%]
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%140["CausalGraph"]
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Graph3D[%]
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LayeredGraphPlot[%147]
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New explorer

Select[Union[Table[RandomWolframModelRule[{{3,2}}{{5,2}},4],50]],NewVerticesQ]
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WolframModelExplorer1[%161,Automatic,10,4]
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WolframModelExplorer1[{{{1,2},{1,2},{1,3}}{{1,4},{2,1},{2,3},{2,4},{4,3}},{{1,2},{1,2},{3,1}}{{2,4},{3,4},{4,1},{4,1},{4,3}},{{1,1},{1,2},{3,3}}{{1,1},{3,1},{3,2},{4,1},{4,4}}},Automatic,20,15]
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Another rule

NOTE: this is an LHS disconnected rule.....
WolframModel[{{{1,1},{1,2},{3,3}}{{1,1},{3,1},{3,2},{4,1},{4,4}}},Table[0,3,2],15]
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HypergraphPlot[%["FinalState"]]
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%%["CausalGraph"]
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LayeredGraphPlot[%]
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HypergraphPlot/@%169["StatesList"]
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RulePlot[WolframModel[{{1,1},{1,2},{3,3}}{{1,1},{3,1},{3,2},{4,1},{4,4}}]]
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RulePlot[WolframModel[{{1,1},{1,2},{3,3}}{{1,1},{3,1},{3,2},{4,1},{4,4}}],VertexLabels->Automatic]
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HypergraphPlot[#,VertexLabelsAutomatic]&/@Take[%169["StatesList"],6]
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GraphPlot[Rule@@@#,PlotTheme"IndexLabeled",VertexSizeMedium]&/@Take[%169["StatesList"],6]
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GraphPlot[Rule@@@#,PlotTheme"IndexLabeled",VertexSize.5]&/@Take[%169["StatesList"],6]
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Select[Union[Table[RandomWolframModelRule[{{3,2}}{{5,2}},4],50]],NewVerticesQ]
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WolframModelExplorer1[%,Automatic,10,4]
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WolframModelExplorer1[{{{1,1},{1,2},{3,2}}{{1,4},{2,3},{3,1},{3,3},{4,1}},{{1,1},{2,1},{2,3}}{{1,3},{2,2},{3,1},{3,4},{4,1}},{{1,2},{1,3},{2,1}}{{1,2},{3,2},{3,4},{4,1},{4,3}}},Automatic,25,10]
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