In[]:=
Table[InteractiveListSelectorSW[First/@GatherBy[SubstitutionSystemCausalGraph[#,"AA",6]#&/@sigsA[n],First]],{n,1,6}]
Out[]=
{{AAAAA},{AAAAA}}
In[]:=
SubstitutionSystemCausalGraph["AA""AAA","AA",14]
Out[]=
In[]:=
GraphPlot[%]
Out[]=
In[]:=
SMWXGraphicsStreamed[SMWEvolveListX[{"AA"->"AAA"},"AA",7],CellLabelsTrue]
Out[]=
In[]:=
SMWEvolveListX[{"AA"->"AAA"},"AA",7]
Out[]=
In[]:=
StringLength/@NestList[StringReplace[#,{"AA"->"AAA"}]&,"AA",20]
Out[]=
{2,3,4,6,9,13,19,28,42,63,94,141,211,316,474,711,1066,1599,2398,3597,5395}
In[]:=
StringLength/@NestList[StringReplace[#,{"AA"->"AAA"}]&,"AA",25]
Out[]=
{2,3,4,6,9,13,19,28,42,63,94,141,211,316,474,711,1066,1599,2398,3597,5395,8092,12138,18207,27310,40965}
In[]:=
Ratios[%488]//N
Out[]=
{1.5,1.33333,1.5,1.5,1.44444,1.46154,1.47368,1.5,1.5,1.49206,1.5,1.49645,1.49763,1.5,1.5,1.4993,1.5,1.49969,1.5,1.49986,1.49991,1.5,1.5,1.49997,1.5}
{2,3,4,6,9,13,19,28,42,63,94,141,211,316,474,711,1066,1599,2398,3597,5395,8092,12138,18207,27310,40965}
In[]:=
NestList[If[EvenQ[#],3#/2,(3#-1)/2]&,2,10]
Out[]=
{2,3,4,6,9,13,19,28,42,63,94}
In[]:=
NestList[(3/2If[EvenQ[#],#,#-1])&,2,10]
Out[]=
{2,3,3,3,3,3,3,3,3,3,3}
In[]:=
FindSequenceFunction[%,t]
Out[]=
DifferenceRootFunction{y.,n.},1+y.[n.]-y.[3+n.]-y.[5+n.]-y.[6+n.]-y.[7+n.]+y.[9+n.]0,y.[1]2,y.[2]3,y.[3]4,y.[4]6,y.[5]9,y.[6]13,y.[7]19,y.[8]28,y.[9]42[t]
In[]:=
FindLinearRecurrence[%%]
Out[]=
{1,1,0,0,-1,1,-1,0,-1,1}
In[]:=
FindLinearRecurrence[%]
Out[]=
FindLinearRecurrence[{2,3,4,6,9,13,19,28,42,63,94,141,211,316,474,711,1066,1599,2398,3597,5395,8092,12138,18207,27310,40965}]
In[]:=
Table[InteractiveListSelectorSW[First/@GatherBy[SubstitutionSystemCausalGraph[#,"AAA",5]#&/@sigsA[n],First]],{n,1,6}]
Out[]=