In[]:=
TSModEvolve[{{0,1,1,1,1,1,1,1,1,0,1,1,0,1},{0}},1000]
Out[]=
{{0,0,1,0,0,0,1,1,1,0,0,0,0,0,0},{0,0}}
In[]:=
PostTagSystemFinalState[{1,{0,1,1,1,1,1,1,1,1,0,1,1,0,1,0}},1000]
Out[]=
{2,{0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0}}
In[]:=
ToModForm[{0,1,1,1,1,1,1,1,1,0,1,1,0,1,0}]
Out[]=
{{0,1,1,0,0},{}}
In[]:=
FromModForm[{{0,1,1,1,1,1,1,1,1,0,1,1,0,1},{0}},_]
Out[]=
{0,_,_,1,_,_,1,_,_,1,_,_,1,_,_,1,_,_,1,_,_,1,_,_,1,_,_,0,_,_,1,_,_,1,_,_,0,_,_,1,_,_,0}
In[]:=
TSDirectEvolve[%51,1000]
Out[]=
{0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
In[]:=
ToModForm[%]
Out[]=
{{0,0,1,0,0,0,1,1,1,0,0,0,0,0,0},{0,0}}
In[]:=
FromModForm[%,_]
Out[]=
{0,_,_,0,_,_,1,_,_,0,_,_,0,_,_,0,_,_,1,_,_,1,_,_,1,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,0}
In[]:=
TSDirectEvolve[%,30]
Out[]=
{1,0,1,1,1,0,1,0,0,0,0,0,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0}
In[]:=
ToModForm[%]
Out[]=
{{1,1,1,0,0,0,1,1,1,0,0},{0,0}}
In[]:=
TSDirectEvolve[{0,_,_,0,_,_,1,_,_,0,_,_,0,_,_,0,_,_,1,_,_,1,_,_,1,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,_,_,1,1},30]
Out[]=
{0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0}
In[]:=
ToModForm[{0,_,_,0,_,_,1,_,_,0,_,_,0,_,_,0,_,_,1,_,_,1,_,_,1,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,0}]
Out[]=
{{0,0,1,0,0,0,1,1,1,0,0,0,0,0,0},{0,0}}
In[]:=
ToModForm[{0,_,_,0,_,_,1,_,_,0,_,_,0,_,_,0,_,_,1,_,_,1,_,_,1,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,_,_,0,_,_,1,1}]
Out[]=
{{0,0,1,0,0,0,1,1,1,0,0,0,0,0,0},{1,1}}
In[]:=
TSModEvolve[{{0,0,1,0,0,0,1,1,1,0,0,0,0,0,0},{1,1}},64]
Out[]=
{{0,0,1,0,1,0,0},{}}
In[]:=
TSModEvolve[{{0,0,1,0,0,0,1,1,1,0,0,0,0,0,0},{0,0}},64]
Out[]=
{{0,0,1,1,1,0,0,0,1,1,1,0},{0}}
In[]:=
TSModEvolve[{{0,0,1,0,0,0,1,1,1,0,0,0,0,0,0},{1,0}},64]
Out[]=
{{0,0,1,0,1,0,0},{}}
In[]:=
PostTagSystemFinalState[{2,{0,0,1,0,0,0,1,1,1,0,0,0,0,0,0}},64]
Out[]=
{1,{1,1,0,0,0,0,1,1}}
In[]:=
PostCycles[halflength_]:=Sort[Flatten[Flatten/@Permutations[#/.{1{0,1},2{1,1,0,0}}]&/@IntegerPartitions[halflength,All,{1,2}],1]];Length[PostCycles[#]]&/@Range[20]
Out[]=
{1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946}
In[]:=
PostCycles[5]
Out[]=
{{0,1,0,1,0,1,0,1,0,1},{0,1,0,1,0,1,1,1,0,0},{0,1,0,1,1,1,0,0,0,1},{0,1,1,1,0,0,0,1,0,1},{0,1,1,1,0,0,1,1,0,0},{1,1,0,0,0,1,0,1,0,1},{1,1,0,0,0,1,1,1,0,0},{1,1,0,0,1,1,0,0,0,1}}
In[]:=
PostCycles[10]
Out[]=
Proof of repetitions....
Proof of repetitions....
Imagine we make the transition matrix from the front of the init to the back of the objects.
In[]:=
TSDirectEvolveList[{1,1,0,1,1,1,0,1,0,0,0,0},30]
Out[]=
{{1,1,0,1,1,1,0,1,0,0,0,0},{1,1,1,0,1,0,0,0,0,1,1,0,1},{0,1,0,0,0,0,1,1,0,1,1,1,0,1},{0,0,0,1,1,0,1,1,1,0,1,0,0},{1,1,0,1,1,1,0,1,0,0,0,0},{1,1,1,0,1,0,0,0,0,1,1,0,1},{0,1,0,0,0,0,1,1,0,1,1,1,0,1},{0,0,0,1,1,0,1,1,1,0,1,0,0},{1,1,0,1,1,1,0,1,0,0,0,0},{1,1,1,0,1,0,0,0,0,1,1,0,1},{0,1,0,0,0,0,1,1,0,1,1,1,0,1},{0,0,0,1,1,0,1,1,1,0,1,0,0},{1,1,0,1,1,1,0,1,0,0,0,0},{1,1,1,0,1,0,0,0,0,1,1,0,1},{0,1,0,0,0,0,1,1,0,1,1,1,0,1},{0,0,0,1,1,0,1,1,1,0,1,0,0},{1,1,0,1,1,1,0,1,0,0,0,0},{1,1,1,0,1,0,0,0,0,1,1,0,1},{0,1,0,0,0,0,1,1,0,1,1,1,0,1},{0,0,0,1,1,0,1,1,1,0,1,0,0},{1,1,0,1,1,1,0,1,0,0,0,0},{1,1,1,0,1,0,0,0,0,1,1,0,1},{0,1,0,0,0,0,1,1,0,1,1,1,0,1},{0,0,0,1,1,0,1,1,1,0,1,0,0},{1,1,0,1,1,1,0,1,0,0,0,0},{1,1,1,0,1,0,0,0,0,1,1,0,1},{0,1,0,0,0,0,1,1,0,1,1,1,0,1},{0,0,0,1,1,0,1,1,1,0,1,0,0},{1,1,0,1,1,1,0,1,0,0,0,0},{1,1,1,0,1,0,0,0,0,1,1,0,1},{0,1,0,0,0,0,1,1,0,1,1,1,0,1}}
In[]:=
Length/@FindTransientRepeat[%,3]
Out[]=
{0,4}
In[]:=
ToModForm/@%113
Out[]=
{{{1,1,0,0},{}},{{1,0,0,1},{1}},{{0,0,1,1},{0,1}},{{0,1,1,0},{0}},{{1,1,0,0},{}},{{1,0,0,1},{1}},{{0,0,1,1},{0,1}},{{0,1,1,0},{0}},{{1,1,0,0},{}},{{1,0,0,1},{1}},{{0,0,1,1},{0,1}},{{0,1,1,0},{0}},{{1,1,0,0},{}},{{1,0,0,1},{1}},{{0,0,1,1},{0,1}},{{0,1,1,0},{0}},{{1,1,0,0},{}},{{1,0,0,1},{1}},{{0,0,1,1},{0,1}},{{0,1,1,0},{0}},{{1,1,0,0},{}},{{1,0,0,1},{1}},{{0,0,1,1},{0,1}},{{0,1,1,0},{0}},{{1,1,0,0},{}},{{1,0,0,1},{1}},{{0,0,1,1},{0,1}},{{0,1,1,0},{0}},{{1,1,0,0},{}},{{1,0,0,1},{1}},{{0,0,1,1},{0,1}}}
In[]:=
Flatten[{1,1,0,0}/.{0{0,0},1{1,1,0,1}}]
Out[]=
{1,1,0,1,1,1,0,1,0,0,0,0}
Sequence testing
Sequence testing
In[]:=
seq1=TSDirectEvolveSequence[{1,0,0,1,0,0,1,0,0,0,0,0},450]
Out[]=
In[]:=
ListStepPlot[Accumulate[(-1)^%]]
Out[]=
In[]:=
seq1=TSDirectEvolveSequence[{1,0,0,1,0,0,1,0,0,0,0,0},450];
In[]:=
Counts[seq1]
Out[]=
1615,0645
In[]:=
Counts[Partition[seq1,2,1]]
Out[]=
{1,0}292,{0,0}353,{0,1}291,{1,1}323
In[]:=
Counts[Partition[seq1,3,1]]
Out[]=
{1,0,0}88,{0,0,1}87,{0,1,0}87,{0,0,0}265,{0,1,1}204,{1,1,0}204,{1,0,1}204,{1,1,1}119
In[]:=
Counts[Partition[seq1,4,1]]
Out[]=
{1,0,0,1}42,{0,0,1,0}2,{0,1,0,0}87,{1,0,0,0}46,{0,0,0,0}219,{0,0,0,1}45,{0,0,1,1}85,{0,1,1,0}85,{1,1,0,1}204,{1,0,1,1}119,{0,1,1,1}119,{1,1,1,0}119,{1,0,1,0}85
In[]:=
Length[{0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0}]
Searches
Searches
From TagSystems-15
Number of random initial conditions out of 10,000 that survive for 5B steps, as a function of initial size:
Initial length len
??? Only half the time does it “reach a highway”
Model
Model
Every initial length has a certain number of random walks “packed inside it”...
Parallel Search
Parallel Search
Known halt states are our cycles.....
Known halt states are our cycles.....
Need PostCyclesQ
[[[ PostTagSystemFinalState FAILS for init of length <9 ]]]
[[[ PostTagSystemFinalState FAILS for init of length <9 ]]]
Significantly smaller:
[[[ Make picture showing intermediate strings .... ]]]
log p ~ log t
[ prediction would be that this survival time ~ 1/Sqrt[t] ]
plateaus are probably related to highways......