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.