Side effects

Select for one trait .... what other “traits” come for free
“Trait” is some computationally bounded measurement

Open endedness

In[]:=
RemoteBatchSubmit[AdaptiveCellularAutomaton[<|"InitialRule"->{0,5,1},"AdaptiveIterations"->100000,"MutationFunction"->(RandomRuleMutation[#BestRule,Ceiling[10/#BestFitness],"Symmetric"->True]&),"MaxSteps"->((Max[#BestFitness,0]+400&))|>,"BreakthroughStates",{"BestRule","BestFitness","Index"},RandomSeeding->898768768675675655756801218]]
Out[]=
RemoteBatchJobObject
Provider:
Wolfram Batch »
 Job type: Single
Job UUID: 5a57d43b-a485-4c24-b3d5-389020de07ad
Input: AdaptiveCellularAutomaton[«4»]
Submitted at: Wed 30 Sep 2026 01:52:14 GMT-4
Geozone: UnitedStates

In[]:=
RemoteBatchSubmit[AdaptiveCellularAutomaton[<|"InitialRule"->{0,5,1},"AdaptiveIterations"->100000,"MutationFunction"->(RandomRuleMutation[#BestRule,Ceiling[10/#BestFitness],"Symmetric"->True]&),"MaxSteps"->((Max[#BestFitness,0]+400&))|>,"BreakthroughStates",{"BestRule","BestFitness","Index"},RandomSeeding->898768768675675655756766621]]
Out[]=
RemoteBatchJobObject
Provider:
Wolfram Batch »
 Job type: Single
Job UUID: a999848b-bc6d-463a-a886-6e4ba43319c4
Input: AdaptiveCellularAutomaton[«4»]
Submitted at: Wed 30 Sep 2026 01:55:54 GMT-4
Geozone: UnitedStates

Row[Labeled[CellularAutomatonPlot[#BestRule,{{1},0},#BestFitness,​​ImageSize->{Automatic,13Sqrt[#BestFitness]},ColorRules->$ColorRules​​],Text[Style[#Index,Small]]]&/@bts]
In[]:=
RemoteBatchJobObject
Provider:
Wolfram Batch »
 Job type: Single
Job UUID: 5a57d43b-a485-4c24-b3d5-389020de07ad
Input: AdaptiveCellularAutomaton[«4»]
Submitted at: Wed 30 Sep 2026 01:52:14 GMT-4
Geozone: UnitedStates
["JobStatus"]
Out[]=
Running
In[]:=
RemoteBatchJobObject["WolframBatch","5a57d43b-a485-4c24-b3d5-389020de07ad"]["EvaluationResult"]
Out[]=
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In[]:=
RemoteBatchJobObject["WolframBatch","a999848b-bc6d-463a-a886-6e4ba43319c4"]["EvaluationResult"]
Out[]=
{BestRule{0,5,1},BestFitness1,Index0,BestRule{794573524998663541181140132650699280816658674271510532666759347950552516644404072623375,5,1},BestFitness3,Index269,BestRule{795330656115482876731755130638219261747014722012323348446250165987317436402698750357625,5,1},BestFitness5,Index277,BestRule{795330655345110897739926890028454393214900376560190258226642405695770853227039668326375,5,1},BestFitness6,Index280,BestRule{795329933121381752526481994053269536118216469699966379972041255874116891034443213217000,5,1},BestFitness7,Index285,BestRule{795336096094738601339725856787910823748813211862758199968541890974645490296225197201375,5,1},BestFitness13,Index298,BestRule{757720276868425401084726287592663048407938934923551178426808479833905572541098244076375,5,1},BestFitness30,Index300,BestRule{757720276637313807758257985225945695297747656698978980640961896405112917073092872982625,5,1},BestFitness43,Index301,BestRule{757720276686001316752367307591200817694764949478054584089252972752344784386477882748250,5,1},BestFitness58,Index311,BestRule{757720276686001316752367307591200817694764949478055472267672672877592024453006203060750,5,1},BestFitness84,Index313,BestRule{757720276686001316752367307591200817694764949478055472267672672868278798706851417904500,5,1},BestFitness181,Index319,BestRule{753958694763369996726867350672089631525745219696384774435276273405683216698489601498250,5,1},BestFitness182,Index344,BestRule{753958694732555117654536900473802551104149353733348897803128426429388101704440568295125,5,1},BestFitness365,Index464,BestRule{753958694716654640033675881270973058954658236040176982070764285862018342621646378842000,5,1},BestFitness665,Index661,BestRule{772766604329811240161175665866528995093712805287907502018245583866295393116794083920125,5,1},BestFitness953,Index947,BestRule{678727056264028237945954932446725730044762430180568040951132577145976002819858048763875,5,1},BestFitness1045,Index975,BestRule{2089320277250773247508438777113420543427161098307073066761634624680076714165530656185750,5,1},BestFitness1375,Index1233,BestRule{2089320277250773247571547649531101488918890567597571388970894265338351007111392472592000,5,1},BestFitness1490,Index1486,BestRule{2089320277250773247887092011619506211083581993710685880840176839381960209019504044857625,5,1},BestFitness1695,Index1539}
In[]:=
rrus=ParallelMapAdaptiveCellularAutomaton[​​<|"InitialRule"->{0,5,1},"AdaptiveIterations"->1000,"MutationFunction"->(RandomRuleMutation[#BestRule,Ceiling[10/#BestFitness],"Symmetric"->True]&),"MaxSteps"->((Max[#BestFitness,0]+400&))|>,​​"FinalState",RandomSeeding->#]&,
[[All,"Seed"]];
In[]:=
GraphicsGrid[Partition[ArrayPlot[CellularAutomaton[#BestRule,{{1},0},Round[#BestFitness1.02]],ImageSize->{Automatic,250},ColorRules->$ColorRules]&/@rrus,UpTo[5]]]
Out[]=

Patch picking