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rulesmap=Module{res,sublevels,vfs},res=Reap[2,2,GraphLayout->"LayeredDigraphEmbedding"],"SubLevels";First/@res[[2,1,1]]
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{0,1}4294901480,{1,1}4009672564,{2,1}4139699108,{3,1}4009672548,{3,2}4139682740,{3,3}1992216484,{4,1}1992200116,{4,2}4009671524,{5,1}2585675684,{5,2}650009444,{6,1}2591958948,{6,2}442263460,{6,3}3460078436,{6,4}784227172,{6,5}2185122660,{7,1}4209549716,{7,2}3871120228,{7,3}2591958964,{7,4}1584180116,{7,5}2453555108,{8,1}1923777940,{8,2}2555536804,{9,1}4005469028,{9,2}370954148,{9,3}2589747108,{10,1}716968804,{11,1}3595086228,{11,2}2484211124,{12,1}2489461140,{12,2}2518289844,{12,3}1823512932,{13,1}2455644084,{13,2}2519337364,{13,3}2623678868,{13,4}3938227044,{14,1}3729303956,{14,2}983172532,{14,3}1449962388,{14,4}3198814612,{15,1}1348772756,{16,1}2552365460,{17,1}649878372,{17,2}2586444180,{17,3}849086372,{18,1}3028421012,{19,1}1019357588,{19,2}2490379700,{19,3}2621581716,{19,4}814745012,{19,5}2585396644,{20,1}848823732,{21,1}2619476372,{22,1}1514709396,{23,1}444344244,{23,2}3662193044,{25,1}2763020644,{25,2}3029470644,{28,1}2417100196,{28,2}3392835940,{39,1}3063549364,{45,1}2417362868,{64,1}2455381412
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CAProfile[{ru_,k_,r_},lt_]:=Map[Length@*ResourceFunction["ArrayCrop"],CellularAutomaton[{ru,k,r},{{1},0},lt]]
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KeyValueMapCAProfile[{#2,2,2},#1[[1]]]&,
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ListStepPlot
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ListStepPlot
,Filling->Axis,FillingStyle->Opacity[.02]
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Max/@KeyValueMapCAProfileB[{#2,2,2},#1[[1]]]&,
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{1,3,5,5,5,5,5,5,7,9,9,9,9,9,9,11,11,9,9,9,11,9,9,9,9,11,15,13,17,13,11,15,17,17,11,15,15,15,19,19,23,19,23,17,25,25,21,27,21,23,21,19,19,25,19,29,21,27,21,35,33,51}
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Histogram[%,{1}]
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KeyValueMap{#1[[1]],Max@CAProfile[{#2,2,2},#1[[1]]]}&,
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{{0,1},{1,3},{2,5},{3,5},{3,5},{3,5},{4,5},{4,5},{5,7},{5,9},{6,9},{6,9},{6,9},{6,9},{6,9},{7,11},{7,11},{7,9},{7,9},{7,9},{8,11},{8,9},{9,9},{9,9},{9,9},{10,11},{11,15},{11,13},{12,17},{12,13},{12,11},{13,15},{13,17},{13,17},{13,11},{14,15},{14,15},{14,15},{14,19},{15,19},{16,23},{17,19},{17,23},{17,17},{18,25},{19,25},{19,21},{19,27},{19,21},{19,23},{20,21},{21,19},{22,19},{23,25},{23,19},{25,29},{25,21},{28,27},{28,21},{39,35},{45,33},{64,51}}
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ListPlot[%]
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BubbleChartAppend[First[#],Length[#]]&/@GatherKeyValueMap{#1[[1]],Max@CAProfile[{#2,2,2},#1[[1]]]}&,
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k=3, r=1 symmetric
k=3, r=1 symmetric
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changeFitness[lifetimes_,{k_,r_},fun_]:=Association[KeyValueMap[Function[{item,lt},item->fun[CellularAutomaton[{item[[1]],k,r},{{1},0},lt+1]]],lifetimes]]
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$LifetimeData[3,1,"Symmetric"]=;
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Iconize[changeFitness[$LifetimeData[3,1,"Symmetric"],{3,1},Last@*Dimensions]]
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widths=%
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lw=Merge,,Identity;
Why aren’t the callouts bigger??
Statistical Measures of the Width Function
Statistical Measures of the Width Function
Path Lengths
Path Lengths
How does one get to a particular rule from the null rule, through actually evolution?
In simple cases, you just sequentially add in the bits [in some order?]