Is there a trace of simplicity in the states?
Is there a trace of simplicity in the states?
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RandomParticleState[80,24]
Out[]=
{1,0,1,0,1,0,1,2,2,0,0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,1,0,2,0,2,2,0,0,0,2,1,0,0,2,0,0,0,2,0,0,0,0,2,0,0,0,2,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,2}
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80-20
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60
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56/2
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28
Join[RandomParticleState[30,4],Table[1,20],RandomParticleState[30,4]]
Out[]=
{0,0,1,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,1,0}
In[]:=
GraphicsRow[Table[ArrayPlot[ResourceFunction["BlockCellularAutomaton"][{{2,2}{1,1},{1,1}{2,2},{1,2}{1,2},{2,1}{2,1},{2,0}{0,2},{1,0}{1,0},{0,2}{2,0},{0,1}{0,1},{0,0}{0,0}},Join[RandomParticleState[30,4],Table[1,20],RandomParticleState[30,4]],350],ColorRules->{0->White,1->Lighter[Orange],2->Darker[Orange]},ImageSize->{Automatic,330}],10]]
Out[]=
In[]:=
GraphicsRow[Table[ArrayPlot[Take[ResourceFunction["BlockCellularAutomaton"][{{2,2}{1,1},{1,1}{2,2},{1,2}{1,2},{2,1}{2,1},{2,0}{0,2},{1,0}{1,0},{0,2}{2,0},{0,1}{0,1},{0,0}{0,0}},Join[RandomParticleState[30,4],Table[1,20],RandomParticleState[30,4]],5000],-350],ColorRules->{0->White,1->Lighter[Orange],2->Darker[Orange]},ImageSize->{Automatic,330}],10]]
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There is a difference from the “walls”......
In[]:=
GraphicsRow[Table[ArrayPlot[ResourceFunction["BlockCellularAutomaton"][{{2,2}{1,1},{1,1}{2,2},{1,2}{1,2},{2,1}{2,1},{2,0}{0,2},{1,0}{1,0},{0,2}{2,0},{0,1}{0,1},{0,0}{0,0}},RandomParticleState[80,24],350],ColorRules->{0->White,1->Lighter[Orange],2->Darker[Orange]},ImageSize->{Automatic,330}],10]]
Out[]=
In[]:=
SeedRandom[42342342];GraphicsRow[Table[ArrayPlot[Take[ResourceFunction["BlockCellularAutomaton"][{{2,2}{1,1},{1,1}{2,2},{1,2}{1,2},{2,1}{2,1},{2,0}{0,2},{1,0}{1,0},{0,2}{2,0},{0,1}{0,1},{0,0}{0,0}},RandomParticleState[80,24],350],-350],ColorRules->{0->White,1->Lighter[Orange],2->Darker[Orange]},ImageSize->{Automatic,330}],10]]
Out[]=
In[]:=
SeedRandom[42342342];GraphicsRow[Table[ArrayPlot[Take[ResourceFunction["BlockCellularAutomaton"][{{2,2}{1,1},{1,1}{2,2},{1,2}{1,2},{2,1}{2,1},{2,0}{0,2},{1,0}{1,0},{0,2}{2,0},{0,1}{0,1},{0,0}{0,0}},RandomParticleState[80,24],5000],-350],ColorRules->{0->White,1->Lighter[Orange],2->Darker[Orange]},ImageSize->{Automatic,330}],10]]
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This makes a wall:
Features:
Features:
Isolated 1s never do anything...
What conservation laws are there??
What conservation laws are there??
Which sums of blocks are conserved?
Imagine there are many conservation laws.... A given state is characterized by its “conserved quantities”
Going 2 steps...
Going 2 steps...
[From NKS https://www.wolframscience.com/nks/notes-9-4--more-general-conserved-quantities/ ]
This is the trivial conservation for block size 1:
Last two are just particle conservation....
So this is again just particle conservation.....
Persistent structures
Persistent structures
Dependence on Initial Conditions
Dependence on Initial Conditions
Correlations
Correlations
Time correlations ....