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In[]:=
IntegerDigits[10,2]
Out[]=
{1,0,1,0}
In[]:=
Boole[BooleanTable[BooleanCountingFunction[{{1,3}},5]]]
Out[]=
{0,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0}
In[]:=
CellularAutomaton[{10,{2,1},2}][#][[3]]&/@Tuples[{1,0},5]
Out[]=
{0,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0}
In[]:=
BooleanMinimize[BooleanCountingFunction[{{1,3}},5][a1,a2,a3,a4,a5]]
Out[]=
(a1&&a2&&a3&&!a4&&!a5)||(a1&&a2&&!a3&&a4&&!a5)||(a1&&a2&&!a3&&!a4&&a5)||(a1&&!a2&&a3&&a4&&!a5)||(a1&&!a2&&a3&&!a4&&a5)||(a1&&!a2&&!a3&&a4&&a5)||(a1&&!a2&&!a3&&!a4&&!a5)||(!a1&&a2&&a3&&a4&&!a5)||(!a1&&a2&&a3&&!a4&&a5)||(!a1&&a2&&!a3&&a4&&a5)||(!a1&&a2&&!a3&&!a4&&!a5)||(!a1&&!a2&&a3&&a4&&a5)||(!a1&&!a2&&a3&&!a4&&!a5)||(!a1&&!a2&&!a3&&a4&&!a5)||(!a1&&!a2&&!a3&&!a4&&a5)
In[]:=
BooleanConvert[%,"Nand"]
Out[]=
(a1⊼a2⊼a3⊼!a4⊼!a5)⊼(a1⊼a2⊼!a3⊼a4⊼!a5)⊼(a1⊼a2⊼!a3⊼!a4⊼a5)⊼(a1⊼!a2⊼a3⊼a4⊼!a5)⊼(a1⊼!a2⊼a3⊼!a4⊼a5)⊼(a1⊼!a2⊼!a3⊼a4⊼a5)⊼(a1⊼!a2⊼!a3⊼!a4⊼!a5)⊼(!a1⊼a2⊼a3⊼a4⊼!a5)⊼(!a1⊼a2⊼a3⊼!a4⊼a5)⊼(!a1⊼a2⊼!a3⊼a4⊼a5)⊼(!a1⊼a2⊼!a3⊼!a4⊼!a5)⊼(!a1⊼!a2⊼a3⊼a4⊼a5)⊼(!a1⊼!a2⊼a3⊼!a4⊼!a5)⊼(!a1⊼!a2⊼!a3⊼a4⊼!a5)⊼(!a1⊼!a2⊼!a3⊼!a4⊼a5)
In[]:=
BooleanConvert[BooleanCountingFunction[{{1,3}},5][a1,a2,a3,a4,a5],"ANF"]
Out[]=
a1⊻a2⊻a3⊻a4⊻a5⊻(a1&&a2&&a3&&a4&&a5)
In[]:=
Boole[BooleanTable[BooleanConvert[BooleanCountingFunction[{{1,3}},5],"ANF"]]]
Out[]=
{0,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0}
In[]:=
InputForm[%124]
Out[]//InputForm=
Xor[a1, a2, a3, a4, a5, a1 && a2 && a3 && a4 && a5]
In[]:=
BooleanConvert[BooleanCountingFunction[{{1,3}},5][a1,a2,a3,a4,a5],"IF"]
Out[]=
If[a1,If[a2,If[a3,If[a4,False,If[a5,False,True]],If[a4,If[a5,False,True],If[a5,True,False]]],If[a3,If[a4,If[a5,False,True],If[a5,True,False]],If[a4,If[a5,True,False],If[a5,False,True]]]],If[a2,If[a3,If[a4,If[a5,False,True],If[a5,True,False]],If[a4,If[a5,True,False],If[a5,False,True]]],If[a3,If[a4,If[a5,True,False],If[a5,False,True]],If[a4,If[a5,False,True],If[a5,True,False]]]]]
In[]:=
BooleanConvert[BooleanCountingFunction[{{1,3}},5][a1,a2,a3,a4,a5],"BFF"]
Out[]=
BooleanFunction[a1,a2,a3,a4,a5]
In[]:=
BooleanConvert[BooleanCountingFunction[{{1,3}},5][a1,a2,a3,a4,a5],"BDT"]
Out[]=
(a1&&!((a2&&((a3&&(a4||(!a4&&a5)))||(!a3&&((a4&&a5)||(!a4&&!a5)))))||(!a2&&((a3&&((a4&&a5)||(!a4&&!a5)))||(!a3&&!((a4&&a5)||(!a4&&!a5)))))))||(!a1&&!((a2&&((a3&&((a4&&a5)||(!a4&&!a5)))||(!a3&&!((a4&&a5)||(!a4&&!a5)))))||(!a2&&!((a3&&((a4&&a5)||(!a4&&!a5)))||(!a3&&!((a4&&a5)||(!a4&&!a5)))))))
In[]:=
BooleanConvert[BooleanCountingFunction[{{1,3}},5][a1,a2,a3,a4,a5],"ESOP"]
Out[]=
(a1&&a2&&a3&&!a4&&!a5)⊻(a1&&a2&&!a3&&a4&&!a5)⊻(a1&&a2&&!a3&&!a4&&a5)⊻(a1&&!a2&&a3&&a4&&!a5)⊻(a1&&!a2&&a3&&!a4&&a5)⊻(a1&&!a2&&!a3&&a4&&a5)⊻(a1&&!a2&&!a3&&!a4&&!a5)⊻(!a1&&a2&&a3&&a4&&!a5)⊻(!a1&&a2&&a3&&!a4&&a5)⊻(!a1&&a2&&!a3&&a4&&a5)⊻(!a1&&a2&&!a3&&!a4&&!a5)⊻(!a1&&!a2&&a3&&a4&&a5)⊻(!a1&&!a2&&a3&&!a4&&!a5)⊻(!a1&&!a2&&!a3&&a4&&!a5)⊻(!a1&&!a2&&!a3&&!a4&&a5)
In[]:=
BooleanConvert[#,"ANF"]&/@NestList[BooleanCountingFunction[{{1,3}},5]@@@Partition[#,5,1]&,Table[a[i],{i,-2,2}],2]
Out[]=
{{a[-2],a[-1],a[0],a[1],a[2]},{a[-2]⊻a[-1]⊻a[0]⊻a[1]⊻a[2]⊻(a[-2]&&a[-1]&&a[0]&&a[1]&&a[2])},{}}
In[]:=
BooleanConvert[#,"ANF"]&/@NestList[BooleanCountingFunction[{{1,3}},5]@@@Partition[Flatten@#,5,1]&,Table[a[i],{i,-4,4}],3]
Out[]=
In[]:=
Count[#,a[_],Infinity]&/@%216
Out[]=
{9,50,716,0}
In[]:=
Count[#,a[_],Infinity]&/@(BooleanConvert[#,"ANF"]&/@NestList[BooleanCountingFunction[{{1,3}},5]@@@Partition[Flatten@#,5,1]&,Table[a[i],{i,-5,5}],4])
Out[]=
{11,70,2148,0,0}
In[]:=
BooleanCountingFunction[{{1,3}},5]@@Table[a[i],{i,-3,3}]
Out[]=
BooleanCountingFunction[{{1,3}},5][a[-3],a[-2],a[-1],a[0],a[1]]
In[]:=
ArrayPlot[CellularAutomaton[{10,{2,1},2},{{1},0},{600,{-600,600}}]]
Out[]=
In[]:=
ArrayPlot[CellularAutomaton[{10,{2,1},2},{{1},0},{{1,600,2},{-600,600,2}}]]
Out[]=
In[]:=
ArrayPlot[CellularAutomaton[{10,{2,1},2},{{1},0},{{1,1200,2},{-1200,1200,2}}]]
Out[]=
In[]:=
ArrayPlot[CellularAutomaton[{376007062,2,2},{{1},0},{{1,1200,2},{-1200,1200,2}}]]
Out[]=
More than one initial 1:
code 22
code 22
Block Simulation
Block Simulation
Look for possible block emulations....
Finding Nested Examples
Finding Nested Examples
Finite size
Finite size
Symmetric states only:
Side repetition
Side repetition
Could decorate with actual sequences...
Center Column
Center Column
Center Column
Center Column
Block entropies
Block entropies
Random
Random
Repeating Blocks
Repeating Blocks