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Lets go back to the original model and try a different initial condition

This model seems like the bare minimum for a meaningful identification of particles. What if we introduce two looping structures?
In[]:=
LayeredGraphPlot
[◼]
MultiwaySystem

[◼]
WolframModel
[{{1,2},{2,1}}{{3,1},{1,3},{2,3}}],{{0,1},{1,0},{1,2},{2,1}},3,"CausalGraph",VertexSize1
Out[]=
LayeredGraphPlot
[◼]
MultiwaySystem

[◼]
WolframModel
[{{1,2},{2,1}}{{3,1},{1,3},{2,3}}],{{0,1},{1,0},{1,2},{2,1}},3,"StatesGraph",VertexSize1
Launching kernels...
ParallelCombine
:No parallel kernels available; proceeding with sequential evaluation.
ParallelCombine
:No parallel kernels available; proceeding with sequential evaluation.
ParallelCombine
:No parallel kernels available; proceeding with sequential evaluation.
General
:Further output of ParallelCombine::nopar will be suppressed during this calculation.
Out[]=
LayeredGraphPlot
[◼]
MultiwaySystem

[◼]
WolframModel
[{{1,2},{2,1}}{{3,1},{1,3},{2,3}}],{{0,1},{1,0},{1,2},{2,1}},3,"EvolutionCausalGraph",VertexSize1
Out[]=
LayeredGraphPlot
[◼]
MultiwaySystem

[◼]
WolframModel
[{{1,2},{2,1}}{{3,1},{1,3},{2,3}}],{{0,1},{1,0},{1,2},{2,1}},3,"EvolutionEventsGraph",VertexSize1
Out[]=
​