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,
13
155
,
189
538
,
1185
4909
,
2239
8259
,
3598
14507
,1,
3
34
,
341
995
,
938
4705
,
653
2697
,
9467
43143

In[]:=
bubxp=Monitor[Transpose[Table[bubp[n],{n,0,10}]],n]
Out[]=
1,
13
155
,
189
538
,
1185
4909
,
2239
8259
,
3598
14507
,
847
3321
,
40975
164721
,
60843
245479
,
118
481
,
81499
335920
,1,
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[a6]
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[]=
{{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,1,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1},
⋯355⋯
,{1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{1,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0}},{
⋯1⋯
}}
Full expression not available
(
original memory size:
379.8 kB)
In[]:=
ArrayPlot/@%189
Out[]=

,

In[]:=
ArrayPlot/@%190
Out[]=

,
