MAToNet4[list_]:=Module[{u},u[_]={∞};Do[u[list〚i〛]={i,u[list〚i〛]},{i,Length[list],1,-1}];MapIndexed[First[#2]First/@{u[#1-1],u[#1]=Last[u[#1]],u[#1+1]}&,list]]
Following is the best version:
MAToNet[list_]:=Module[{u,j,k},u[_]=Infinity;Reverse[Table[j=list[[i]];k=u[j];u[j]=i;i->{u[j-1],k,u[j+1]},{i,Length[list],1,-1}]]]
NeighborCountsI[g_,i0_,n_]:=Map[If[MemberQ[#,Infinity],Infinity,Length[#]]&,Module[{gp=Dispatch[Prepend[g,∞->{∞}]]},NestList[Union[Flatten[{#,#/.gp}]]&,{i0},n]]]
MMAPositionsList[rules_,init_List,t_Integer]:=Module[{m=Dispatch[rules],a=init},Prepend[Table[Last[a=MMAStep[m,a]],{t}],Last[init]]]
MAInitialState[n_]:={Table[0,{n}],(n-1)/2+1}
MMAStep[rules_,{tape_List,pos_Integer}]:=({FlattenAt[Insert[Drop[tape,{pos-1,pos+1}],#1,pos-1],pos-1],pos+#2}&)@@(If[2<=pos<=Length[tape]-1,Take[tape,{pos-1,pos+1}],Abort[]]/.rules)
Differences[list_]:=Drop[list,1]-Drop[list,-1]
MMAPositionsList[mrs[[3]],MAInitialState[1001],2000];
MAToNet4[%];
NeighborCountsI[%,1,30]
{1,4,9,16,27,46,68,95,124,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞}
MMAPositionsList[mrs[[3]],MAInitialState[2001],10000];
MAToNet4[%482];
NeighborCountsI[%,1,30]
{1,4,9,16,27,46,68,95,124,162,207,262,326,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞,∞}
Select[%485,IntegerQ]
{1,4,9,16,27,46,68,95,124,162,207,262,326}
Differences[%]
{3,5,7,11,19,22,27,29,38,45,55,64}
ListPlot[%,PlotJoined->True];
MMAPositionsList[mrs[[4]],MAInitialState[801],2000];
MAToNet4[%];
NeighborCountsI[%,1,30]
{1,4,10,19,29,46,65,88,116,148,181,221,272,317,368,421,482,543,604,672,749,821,899,985,1080,∞,∞,∞,∞,∞,∞}
Select[%,IntegerQ]
{1,4,10,19,29,46,65,88,116,148,181,221,272,317,368,421,482,543,604,672,749,821,899,985,1080}
ListPlot[Differences[%23],PlotJoined->True];
MMAPositionsList[mrs[[2]],MAInitialState[801],2000];
MAToNet4[%];
NeighborCountsI[%,1,30]
{1,4,9,17,29,44,62,84,108,135,165,199,235,274,316,362,410,461,515,573,633,696,762,∞,∞,∞,∞,∞,∞,∞,∞}
Select[%,IntegerQ]
{1,4,9,17,29,44,62,84,108,135,165,199,235,274,316,362,410,461,515,573,633,696,762}
ListPlot[Differences[%],PlotJoined->True];
Install["MobileAutomata`zmalink`"]
LinkObject[".\MobileAutomata\zmalink.exe\Windows\zmalink.exe",6,4]
MAToNet[list_]:=Module[{u,j,k},u[_]=Infinity;Reverse[Table[j=list[[i]];k=u[j];u[j]=i;i->{u[j-1],k,u[j+1]},{i,Length[list],1,-1}]]]
MMAPositionsList[mrs[[3]],MAInitialState[41],20]
{21,22,21,20,19,20,21,22,23,24,23,22,21,22,21,22,23,22,23,24,23}
MAToNet4[%]
{1{4,3,2},2{3,8,9},3{4,7,8},4{5,6,7},5{∞,∞,6},6{∞,∞,7},7{∞,13,8},8{13,12,9},9{12,11,10},10{11,20,∞},11{12,17,20},12{13,14,17},13{∞,15,14},14{15,16,17},15{∞,∞,16},16{∞,18,17},17{18,19,20},18{∞,∞,19},19{∞,21,20},20{21,∞,∞},21{∞,∞,∞}}
MAToNet5[%37]
{1{4,3,2},2{3,8,9},3{4,7,8},4{5,6,7},5{∞,∞,6},6{∞,∞,7},7{∞,13,8},8{13,12,9},9{12,11,10},10{11,20,∞},11{12,17,20},12{13,14,17},13{∞,15,14},14{15,16,17},15{∞,∞,16},16{∞,18,17},17{18,19,20},18{∞,∞,19},19{∞,21,20},20{21,∞,∞},21{∞,∞,∞}}