In[]:=
(((#2-#1+1)&@@nonzeroRange[#])&/@CellularAutomaton[#BestRule,{{1},0},#BestFitness-1])&/@Take[$LifetimeRules,3]
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ListStepPlot
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In[]:=
bigres=BinCounts[#,{0,100,1}]&/@Transpose[ParallelMap[PadRight[((((#2-#1)/2+1)&@@nonzeroRange[#])&/@CellularAutomaton[#BestRule,{{1},0},#BestFitness-1]),200]&,$LifetimeRules]];
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ArrayPlotLog1+
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ListPlot3DLog1+
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bigres1k=BinCounts[#,{0,500,1}]&/@Transpose[ParallelMap[PadRight[((((#2-#1)/2+1)&@@nonzeroRange[#])&/@CellularAutomaton[#BestRule,{{1},0},#BestFitness-1]),1000]&,$LifetimeRules]];
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ListPlot3D[Log[1+bigres1k]]
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Min[Log[1+bigres1k]]
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0
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Max[Log[1+bigres1k]]
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Log[102001]
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N[%]
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11.5327
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MatrixPlot[Log[1+bigres1k],ColorFunctionScaling->False,ColorFunction->(If[#==0,White,Blend[{StandardBlue,StandardRed},#/12]]&)]
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What fraction of the way down is the maximum width?
What fraction of the way down is the maximum width?
only odd widths
erf(x/Sqrt[2 t]) ≈ Sqrt[2/(π t)] x
What is the distribution of width vs. length?
What is the distribution of width vs. length?
Side effect of width
Side effect of width
Perimeter
Perimeter
Qualitative Classification
Qualitative Classification
Straight edges or not?
Straight edges or not?
At what angle?
Tapering or not?
Tapering or not?
Holey or not? I.e. density of nonzero cells
Holey or not? I.e. density of nonzero cells
Symbolic Dynamics of Boundaries
Symbolic Dynamics of Boundaries
On a particular scale, what is the sequence of in/out sections