Cycles for Rule 22

In the process of surveying Rule 22, the following table of cycles N (row number) versus periods P (column number) was found. In counting the number of rings with each period, the zero ring was discounted because it occurs for every value of N; likewise a ring was not repeated if its period was a proper divisor of P, nor was redundancy due to shifting or reflection included (thus it is a table of cycle classes).

      | 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 
   ---+-----------------------------------------------------------
    1 | .  1  .  1  .  1  .  1  .  1  .  1  .  1  .  1  .  1  .  1 
    2 | .  .  .  1  .  .  .  1  .  .  .  1  .  .  .  1  .  .  .  1 
    3 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
    4 | .  .  .  .  .  .  .  1  1  2  1  1  .  .  .  1  1  3  3  5 
    5 | .  .  .  .  .  .  .  .  .  .  1  1  1  .  .  .  .  .  .  . 
    6 | .  .  .  .  .  .  .  1  .  1  .  .  .  .  .  1  .  .  .  2 
    7 | .  .  .  .  .  .  1  .  .  .  .  .  .  1  .  .  .  .  .  . 
    8 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1 
    9 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   10 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   11 | .  .  .  .  .  .  .  .  .  .  1  .  .  .  .  .  .  .  .  . 
   12 | .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  2  1  2  1  1 
   13 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   14 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  .  .  . 
   15 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   16 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   17 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   18 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  . 
   19 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   20 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  .  .  .  .

      |15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 
   ---+-----------------------------------------------------------
   21 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   22 | .  .  .  .  .  .  .  1  .  .  .  .  .  .  .  .  .  .  .  . 
   23 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   24 | .  .  .  1  .  1  .  .  .  1  .  .  .  .  .  .  .  .  .  1 
   25 | .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  .  .  .  .  . 
   26 | .  .  1  .  .  .  .  .  .  .  1  .  1  .  .  .  .  .  .  1 
   27 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   28 | .  .  .  .  1  .  .  .  .  1  1  3  1  3  .  .  .  3  3  6 
   29 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  .  .  .  . 
   30 | .  .  .  .  .  .  .  .  .  .  .  .  1  1  1  .  .  1  .  . 
   31 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  .  . 
   32 | .  .  .  .  .  .  .  .  .  1  .  .  .  .  .  .  .  1  .  . 
   33 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
   34 | .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  .

In addition, there were many cycles in the range with longer periods than convenient for a table, which are listed below.