In[]:=
mapps
Out[]=
{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}{{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0}{{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0}}
As a function of Hamming distance ...
From these inits ...
In[]:=
hams[{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},1]
Out[]=
{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
Probability that we go to a given attractor as a function of the Hamming distance of its standard inputs
Adding errors to the initial condition, what is the probability that we still go to the correct attractor....
In[]:=
allprobs[rmap_,key_,list_,n_]:=Mean[Boole[key==evalfun[rmap,#]]&/@(Union@@(hams[#,n]&/@list))]
In[]:=
bubp[n_]:=KeyValueMap[allprobs[rulemap,#1,#2,n]&,mapps]
In[]:=
bubp[1]
Out[]=
,
13
155
3
34
In[]:=
bubxp=Monitor[Transpose[Table[bubp[n],{n,0,5}]],n]
Out[]=
1,,,,,,1,,,,,
13
155
189
538
1185
4909
2239
8259
3598
14507
3
34
341
995
938
4705
653
2697
9467
43143
In[]:=
bubxp=Monitor[Transpose[Table[bubp[n],{n,0,10}]],n]
Out[]=
1,,,,,,,,,,,1,,,,,,,,,,
13
155
189
538
1185
4909
2239
8259
3598
14507
847
3321
40975
164721
60843
245479
118
481
81499
335920
3
34
341
995
938
4705
653
2697
9467
43143
7081
30898
37186
164565
56144
245425
71808
310715
39357
167959
In[]:=
ListStepPlot[%,PlotRange->All]
Out[]=
In[]:=
allok[rmap_,key_,list_,n_]:=Select[(Union@@(hams[#,n]&/@list)),key==evalfun[rmap,#]&]
In[]:=
Boole[a==6]
Out[]=
Boole[a6]
In[]:=
With[{n=1},KeyValueMap[allok[rulemap,#1,#2,n]&,mapps]]
Out[]=
{{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0},{0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},{0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1},{0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}}
In[]:=
With[{n=2},KeyValueMap[allok[rulemap,#1,#2,n]&,mapps]]
Out[]=
In[]:=
ArrayPlot/@%189
Out[]=
,
In[]:=
ArrayPlot/@%190
Out[]=
,