LayeredGraphPlot[HighlightGraph[MultiwaySystem[{"A""AB","B""A"},{"A"},7,"StatesGraphStructure"],VertexList[GenerationalMultiwaySystem[{"A""AB","B""A"},{"A"},5,"StatesGraph"]]],AspectRatio1/2]
In[]:=
Out[]=
LayeredGraphPlot[HighlightGraph[MultiwaySystem[{"A""AA","A""BB"},{"AA"},5,"StatesGraphStructure"],VertexList[GenerationalMultiwaySystem[{"A""AA","A""BB"},{"AA"},5,"StatesGraph"]]],AspectRatio1/2]
In[]:=
Graph[GenerationalMultiwaySystem[{"A""AA","A""B"},{"A"},3,"StatesGraph"],AspectRatio1/2]
In[]:=
Out[]=
GraphNeighborhoodVolumes[%,{"A"}]
In[]:=
A{1,3,7,29}
Out[]=
GenerationalMultiwaySystem[{"A""AA","A""B"},{"A"},4,"StatesGraphStructure"]
In[]:=
Out[]=
GraphNeighborhoodVolumes[%,{"A"}]
In[]:=
A{1,3,7,29,473}
Out[]=
gg5=GenerationalMultiwaySystem[{"A""AA","A""B"},{"A"},5,"StatesGraphStructure"];
In[]:=
This rule is not causal invariant....
FindSequenceFunction[{1,3,7,29,473},n]
In[]:=
FindSequenceFunction[{1,3,7,29,473},n]
Out[]=
GraphNeighborhoodVolumes[gg5,{"A"}]

Growth rates of generational multiway systems

EnumerateSubstitutionSystemRules[{12,12},2]
GraphNeighborhoodVolumes[MultiwaySystem[{"A""AB","A""BB"},{"AA"},20,"StatesGraph"],{"AA"}]
cirules=Import["/Users/sw/Dropbox/Physics/Data/MWCausalInvariantSamples/samples-01.wxf"];
In[]:=
Length[cirules]
In[]:=
12
Out[]=
First[cirules]
In[]:=
{}
Out[]=
Take[cirules,4]
In[]:=
Out[]=
ParallelMapMonitored[Labeled[TimeConstrained[GenerationalMultiwaySystem[#,{#[[1,1]]},5,"StatesGraphStructure"],5],#]&,#]&/@Take[cirules,4]
In[]:=
Out[]=
ParallelMapMonitored[Labeled[TimeConstrained[GenerationalMultiwaySystem[#,{#[[1,1]]},5,"StatesGraphStructure"],5],#]&,cirules[[5]]]
In[]:=
Subsets::toomany:The number of subsets (​18446744073709551616​) indicated by Subsets[{AAAA{1,1},AAAA{2,2},AAAA{3,3},AAAA{4,4},AAAA{5,5},AAAA{6,6},AAAA{7,7},AAAA{8,8},AAAA{9,9},AAAA{10,10},AAAA{11,11},29,AAAA{41,41},AAAA{42,42},AAAA{43,43},AAAA{44,44},AAAA{45,45},AAAA{46,46},AAAA{47,47},AAAA{48,48},AAAA{49,49},AAAA{50,50},14}] is too large; it must be a machine integer.
(kernel 64)
Subsets::toomany:The number of subsets (​18446744073709551616​) indicated by Subsets[{AAAA{1,1},AAAA{2,2},AAAA{3,3},AAAA{4,4},AAAA{5,5},AAAA{6,6},AAAA{7,7},AAAA{8,8},AAAA{9,9},AAAA{10,10},AAAA{11,11},29,AAAA{41,41},AAAA{42,42},AAAA{43,43},AAAA{44,44},AAAA{45,45},AAAA{46,46},AAAA{47,47},AAAA{48,48},AAAA{49,49},AAAA{50,50},14}] is too large; it must be a machine integer.
(kernel 64)
Subsets::normal:Nonatomic expression expected at position 1 in Subsets[64].
(kernel 64)
Subsets::argb:Subsets called with 0 arguments; between 1 and 3 arguments are expected.
(kernel 64)
Catenate::invrp:The argument Subsets[] is not a valid Association or a list.
(kernel 64)
GatherBy::list:List expected at position 1 in GatherBy[Catenate[{Subsets[]}],First].
(kernel 64)
Part::partd:Part specification First〚1,1〛 is longer than depth of object.
(kernel 64)
Sort::normal:Nonatomic expression expected at position 1 in Sort[First].
(kernel 64)
GatherBy::list:List expected at position 1 in GatherBy[Subsets[]Catenate[Subsets[]],First〚1,1〛Sort[First]].
(kernel 64)
GatherBy::list:List expected at position 1 in GatherBy[First〚1,1〛Sort[First],Subsets[]Catenate[Subsets[]]].
(kernel 64)
General::stop:Further output of GatherBy::list will be suppressed during this calculation.
(kernel 64)
Catenate::invrp:The argument GatherBy[First〚1,1〛Sort[First],Subsets[]Catenate[Subsets[]]] is not a valid Association or a list.
(kernel 64)
Part
:Part specification First〚1,1〛 is longer than depth of object.
Subsets
:Subsets called with 0 arguments; between 1 and 3 arguments are expected.
GatherBy
:List expected at position 1 in GatherBy[First〚1,1〛,Subsets[]].
Out[]=
ParallelMapMonitored[Labeled[TimeConstrained[GenerationalMultiwaySystem[#,{#[[1,1]]},5,"StatesGraphStructure"],5],#]&,cirules[[6]]]
In[]:=
General
:Further output of GatherBy::list will be suppressed during this calculation.
Out[]=

Combined LHSs as ICs:

ParallelMapMonitored[Labeled[TimeConstrained[GenerationalMultiwaySystem[#,{StringJoin[First/@#]},5,"StatesGraphStructure"],5],#]&,#]&/@Take[cirules,4]
In[]:=
Out[]=
GenerationalMultiwaySystem[{"A""A","A""B"},{"AA"},6,"StatesGraph"]
In[]:=
Out[]=
ParallelMapMonitored[Labeled[TimeConstrained[GenerationalMultiwaySystem[#,{StringJoin[First/@#,First/@#]},4,"StatesGraphStructure"],5],#]&,#]&/@Take[cirules,4]
In[]:=
Out[]=
ParallelMapMonitored[Labeled[TimeConstrained[GenerationalMultiwaySystem[#,{StringJoin[First/@#,First/@#]},4,"StatesGraphStructure"],5],#]&,cirules[[5]]]
In[]:=
Out[]=
RandomSample[Last[cirules],10]
In[]:=
Out[]=
ParallelMapMonitored[Labeled[TimeConstrained[GenerationalMultiwaySystem[#,{StringJoin[First/@#]},4,"StatesGraphStructure"],3],#]&,%153]
In[]:=
Subsets::toomany:The number of subsets (​9444732965739290427392​) indicated by Subsets[{AAAAAA{1,1},AAAAAA{2,2},AAAAAA{3,3},AAAAAA{4,4},AAAAAA{5,5},AAAAAA{6,6},AAAAAA{7,7},AAAAAA{8,8},AAAAAA{9,9},AAAAAA{10,10},32,AAAAAA{43,43},AAAAAA{44,44},AAAAAA{45,45},AAAAAA{46,46},AAAAAA{47,47},AAAAAA{48,48},AAAAAA{49,49},AAAAAA{50,50},23}] is too large; it must be a machine integer.
(kernel 61)
Subsets::argb:Subsets called with 0 arguments; between 1 and 3 arguments are expected.
(kernel 61)
Subsets::argb:Subsets called with 0 arguments; between 1 and 3 arguments are expected.
(kernel 61)
Subsets::toomany:The number of subsets (​590295810358705651712​) indicated by Subsets[{AAAAAA{1,1},AAAAAA{2,2},AAAAAA{3,3},AAAAAA{4,4},AAAAAA{5,5},AAAAAA{6,6},AAAAAA{7,7},AAAAAA{8,8},AAAAAA{9,9},AAAAAA{10,10},32,AAAAAA{43,43},AAAAAA{44,44},AAAAAA{45,45},AAAAAA{46,46},AAAAAA{47,47},AAAAAA{48,48},AAAAAA{49,49},AAAAAA{50,50},19}] is too large; it must be a machine integer.
(kernel 61)
Subsets::argb:Subsets called with 0 arguments; between 1 and 3 arguments are expected.
(kernel 61)
General::stop:Further output of Subsets::argb will be suppressed during this calculation.
(kernel 61)
General::nomem:The current computation was aborted because there was insufficient memory available to complete the computation.
(kernel 61)
Throw::sysexc:Uncaught SystemException returned to top level. Can be caught with Catch[…, _SystemException].
(kernel 61)
Parallel`Developer`QueueRun
::hmm
:Received unexpected result SystemException[MemoryAllocationFailure] from KernelObject
Name: \macpro-basement
KernelID: \61
.
General::nomem:The current computation was aborted because there was insufficient memory available to complete the computation.
(kernel 56)
Throw::sysexc:Uncaught SystemException returned to top level. Can be caught with Catch[…, _SystemException].
(kernel 56)
Parallel`Developer`QueueRun
::hmm
:Received unexpected result SystemException[MemoryAllocationFailure] from KernelObject
Name: \macpro-basement
KernelID: \56
.
General::nomem:The current computation was aborted because there was insufficient memory available to complete the computation.
(kernel 62)
Throw::sysexc:Uncaught SystemException returned to top level. Can be caught with Catch[…, _SystemException].
(kernel 62)
Parallel`Developer`QueueRun
::hmm
:Received unexpected result SystemException[MemoryAllocationFailure] from KernelObject
Name: \macpro-basement
KernelID: \62
.
General
:Further output of Parallel`Developer`QueueRun::hmm will be suppressed during this calculation.
$Aborted
Out[]=
Union[Join[StringJoin/@(Table[IntegerDigits[k,2,4],{k,0,15}]/.{0"B",1"AA"}),StringJoin/@(Table[Prepend[IntegerDigits[k,2,2],0],{k,0,7}]/.{0"B",1"AA"}),StringJoin/@(Table[Append[IntegerDigits[k,2,2],0],{k,0,7}]/.{0"B",1"AA"})]]

Rapid growth case

Union[Flatten[Table[StringJoin/@(Table[IntegerDigits[k,2,g],{k,0,2^g-1}]/.{0"B",1"AA"}),{g,2,8,2}]]]
In[]:=
Out[]=
GenerationalMultiwaySystem[{"A""AA","A""B"},{"A"},4]
In[]:=
Out[]=
Map[StringLength,%,{2}]
In[]:=
Out[]=
Histogram/@%
In[]:=
Out[]=
Union[Flatten[Table[StringJoin/@(Table[IntegerDigits[k,2,g],{k,0,2^g-1}]/.{0"B",1"AA"}),{g,2,3,2}]]]
In[]:=
{AAAA,AAB,BAA,BB}
Out[]=
{"AAAA","AAB","B","BAA","BB"}
Table[Union[Flatten[Table[StringJoin/@(Table[IntegerDigits[k,2,g],{k,0,2^g-1}]/.{0"B",1"AA"}),{g,2,t,2}]]],{t,5}]
In[]:=
{{},{AAAA,AAB,BAA,BB},{AAAA,AAB,BAA,BB},{AAAA,AAAAAAAA,AAAAAAB,AAAABAA,AAAABB,AAB,AABAAAA,AABAAB,AABBAA,AABBB,BAA,BAAAAAA,BAAAAB,BAABAA,BAABB,BB,BBAAAA,BBAAB,BBBAA,BBBB},{AAAA,AAAAAAAA,AAAAAAB,AAAABAA,AAAABB,AAB,AABAAAA,AABAAB,AABBAA,AABBB,BAA,BAAAAAA,BAAAAB,BAABAA,BAABB,BB,BBAAAA,BBAAB,BBBAA,BBBB}}
Out[]=
Complement[%189[[4]],Union[Flatten[Table[StringJoin/@(Table[IntegerDigits[k,2,g],{k,0,2^g-1}]/.{0"B",1"AA"}),{g,2,8,2}]]]]
In[]:=
{AAAAB,AABB,B,BAAAA,BAAB,BBAA,BBB}
Out[]=
Complement[%189[[4]],Union[Flatten[Table[StringJoin/@(Table[IntegerDigits[k,2,g],{k,0,2^g-1}]/.{0"B",1"AA"}),{g,8,8,2}]]]]
In[]:=
{AAAAAAAA,AAAAAAB,AAAAB,AAAABAA,AAAABB,AABAAAA,AABAAB,AABB,AABBAA,AABBB,B,BAAAA,BAAAAAA,BAAAAB,BAAB,BAABAA,BAABB,BB,BBAA,BBAAAA,BBAAB,BBB,BBBAA,BBBB}
Out[]=
Complement[Flatten[%189],Union[Flatten[Table[StringJoin/@(Table[IntegerDigits[k,2,g],{k,0,2^g-1}]/.{0"B",1"AA"}),{g,2,8,2}]]]]
In[]:=
Out[]=