Particle Soup 1
Particle Soup 1
In[]:=
$Rule={{y,x},{z,y}}{{y,w},{z,x},{w,x},{w,z}};
After 15 iterations particles start to appear... increased iterations see particles growing, colliding, increasing. Computationally impossible after 15 steps...
In[]:=
$Plot=GraphPlot$FinalState=ResourceFunction["HypergraphToGraph"][$Rule,{{0,0},{0,0}},15,"FinalState"(*,"EventOrderingFunction"$Methods[[3]]*)];
In[]:=
Rasterize[$Plot,ImageResolution48]
Out[]=
In[]:=
$MyVerts=VertexList[$FinalState];$MyNeighborhoods=NeighborhoodGraph[$FinalState,#]&/@Range[$MyVerts//Length];$RecurringParticles=Cases[{#,Length[#]}&/@GatherBy[$MyNeighborhoods,Quiet[CanonicalGraph[#]]&],{_,a_}/;a>1];
Look at all recurring neighborhoods (structures)....
In[]:=
SortBy[{CanonicalGraph[#[[1,1]]],#[[-1]]}&/@$RecurringParticles,Last]//Reverse
Out[]=
,15618,
,118,
,32,
,12,
,9,
,7,
,6,
,5,
,4,
,3,
,3,
,2,
,2,
,2,
,2,
,2,
,2,
,2,
,2,
,2
Selecting for the densest isomorphic neighborhoods...
In[]:=
$DenseParticles=Select[$RecurringParticles,(5>#[[-1]]>1)&&VertexCount[#[[1,1]]]>50&];
Isomorphic neighborhoods mapped back onto the original graph, colored by kind:
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Rasterize[GraphPlot[HighlightGraph[$FinalState,$DenseParticles[[All,1]]]],ImageResolution48]
Out[]=
The densest neighborhoods need to have many many times more particles / edges (energy) than the non-particle portions of the graph to mirror the actual structure of space:
In[]:=
$UniversalDensity=N@GraphDensity[$FinalState]
Out[]=
0.000126
In[]:=
$DenseParticleDensity=N@GraphDensity[#[[1,1]]]&/@$DenseParticles
Out[]=
{0.00764776,0.00767711,0.0149237,0.0291723}
In the first few iterations of this rule we see repeated dense structures with densities many times that of the overall graph:
In[]:=
$DenseParticleDensity/$UniversalDensity
Out[]=
{60.6964,60.9294,118.442,231.526}
Is this a sensible requirement for discovering a universe like ours?
Do the various Wolfram Graph properties that are exciting when it comes to explaining the foundations of physics extend to particle like mega-structures?
Do the various Wolfram Graph properties that are exciting when it comes to explaining the foundations of physics extend to particle like mega-structures?