The Almost-Center Column of Rule 73

Rule 73 evolving from a single black cell:
In[]:=
ArrayPlot[CellularAutomaton[73,{{1},0},50]]
Out[]=
In[]:=
ArrayPlot[CellularAutomaton[73,{{1},0},500],PixelConstrained1]
Out[]=
The center column is periodic:
In[]:=
CellularAutomaton[73,{{1},0},{50,{{0}}}]
Out[]=
{1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1}
But the column to the right (or left) is not:
In[]:=
CellularAutomaton[73,{{1},0},{50,{{1}}}]
Out[]=
{0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1}
There are about 4 times as many 0s as 1s:
In[]:=
Counts[CellularAutomaton[73,{{1},0},{500,{{1}}}]]
Out[]=
0401,1100
That’s because every other cell is 0:
In[]:=
Take[CellularAutomaton[73,{{1},0},{50,{{1}}}],{2,-1,2}]
Out[]=
{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}
Extract only every other cell in the column to the right:
In[]:=
CellularAutomaton[73,{{1},0},{{2,100,2},{{1}}}]
Out[]=
{0,1,0,0,0,0,1,0,0,1,1,0,0,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0}
There seem to be slightly more 0s than 1s:
In[]:=
Counts[CellularAutomaton[73,{{1},0},{{2,10000,2},{{1}}}]]
Out[]=
02978,12022
In[]:=
Counts[CellularAutomaton[73,{{1},0},{{2,100000,2},{{1}}}]]
Out[]=
029973,120027
In[]:=
Counts[CellularAutomaton[73,{{1},0},{{2,10^6,2},{{1}}}]]
Out[]=
0300462,1199538
The ratio is close to 1.5:
In[]:=
%[0]/%[1]//N
Out[]=
1.50579
Different pairs have different frequencies:
In[]:=
Counts[Partition[CellularAutomaton[73,{{1},0},{{2,10000,2},{{1}}}],2,1]]
Out[]=
{0,1}983,{1,0}982,{0,0}1995,{1,1}1039
Visualizing the evolution showing only every other cell:
In[]:=
ArrayPlot[Downsample[CellularAutomaton[73,{{1},0},1000],{2,2}],PixelConstrained1]
Out[]=
About the rule 73 pattern from A New Kind of Science:
“The pattern has a few definite regularities. The center column of cells is repetitive, alternating between black and white on successive steps. And in all cases black cells appear only in blocks that are an odd number of cells wide. (Any block in rule 73 consisting of an even number of black cells will evolve to a structure that remains fixed forever, as mentioned on page 954.) The more complicated central region of the pattern grows 4 cells every 7 steps; the outer region consists of blocks that are 12 cells wide and repeat every 3 steps.”