Amos Satterlee

Row 2 Notes

There is a distinction to be made between the primary cells and the secondary cells in a pattern. The primary cells are those that are directly activated by the ruleset and are bounded by the ruleset pyramid. The secondary cells are the "background" cells which are either Rule 0 (0:000) or Rule 7 ( 7:111 ) stretching out to infinity (or bouncing back from a boundary).

Row 2 is made up of five primary cells. While the First Row has one arrangement of rules for all 256 rulesets, the 2nd Row has sixteen arrangements, one for each Result Group:

RG-00 0 0 0 0 0
RG-01 0 0 1 2 4
RG-02 0 1 2 4 0
RG-03 0 1 3 6 4
RG-04 1 2 4 0 0
RG-05 1 2 5 2 4
RG-06 1 3 6 4 0
RG-07 1 3 7 6 4
RG-08 6 4 0 1 3
RG-09 6 4 1 3 7
RG-10 6 5 2 5 3
RG-11 6 5 3 7 7
RG-12 7 6 4 1 3
RG-13 7 6 5 3 7
RG-14 7 7 6 5 3
RG-15 7 7 7 7 7

Of note, the rule used in the center is the same as the Result Group number for the first eight groups. The pattern of rules used then repeats where Result Group number minus eight equals the center rule used.

Only four rules are used to invoke the left end cells. They are 0:000,  1:001 ,  6:110 , and  7:111 . Each rule is invoked 64 times (64 x 4 = 256).

Similarly, only four rules are used to invoke the right end cells. They are 0:000,  3:011 ,  4:100 , and  7:111 . Again, each rule is invoked 64 times.

Rules  2:010  and  5:101  are not (and cannot be) used to invoike outside cells.

This is an adjacency chart, showing which rules are adjacent to each other in the 2nd row. Note that 0:000 and  7:111  are the only rules which are sometimes adjacent to themselves.

  0 1 2 3 4 5 6 7
0
1
2
3
4
5
6
7

Here's a tiling pattern riffing on the adjacency table. Here's another.

Analyzing each Result Group pattern, taking into account whether the rules invoke active or passive target cells:

RG-00 00 00 00 00 00

RG-01 00 00 10 20 41

RG-02 00 10 21 40 00

RG-03 00 10 30 60 41
00 10 31 60 41
00 10 30 61 41
00 10 31 61 41

RG-04 11 20 40 00 00

RG-05 11 20 50 20 41
11 20 51 20 41

RG-06 11 30 60 40 00
11 31 60 40 00
11 30 61 40 00
11 31 61 40 00

RG-07 11 30 70 60 41
11 31 70 60 41
11 30 70 61 41
11 31 70 61 41
11 30 71 60 41
11 31 71 60 41
11 30 71 61 41
11 31 71 61 41

RG-08 60 40 01 10 30
60 40 01 10 31
61 40 01 10 30
61 40 01 10 31

RG-09 60 41 10 30 70
60 41 10 31 70
61 41 10 30 70
61 41 10 31 70
60 41 10 30 71
60 41 10 31 71
61 41 10 30 71
61 41 10 31 71

RG-10 60 50 21 50 30
60 50 21 50 31
60 51 21 51 30
60 51 21 51 31
61 50 21 50 30
61 50 21 50 31
61 51 21 51 30
61 51 21 51 31

RG-11 60 50 30 70 70
60 50 31 70 70
60 51 30 70 70
60 51 31 70 70
61 50 30 70 70
61 50 31 70 70
61 51 30 70 70
61 51 31 70 70
60 50 30 71 71
60 50 31 71 71
60 51 30 71 71
60 51 31 71 71
61 50 30 71 71
61 50 31 71 71
61 51 30 71 71
61 51 31 71 71

RG-12 70 60 40 11 30
70 60 40 11 31
70 61 40 11 30
70 61 40 11 31
71 60 40 11 30
71 60 40 11 31
71 61 40 11 30
71 61 40 11 31

RG-13 70 60 50 30 70
70 60 50 31 70
70 60 51 30 70
70 60 51 31 70
70 61 50 30 70
70 61 50 31 70
70 61 51 30 70
70 61 51 31 70
71 60 50 30 70
71 60 50 31 70
71 60 51 30 70
71 60 51 31 70
71 61 50 30 70
71 61 50 31 70
71 61 51 30 70
71 61 51 31 70

RG-14 70 70 60 50 30
70 70 60 50 31
70 70 60 51 30
70 70 60 51 31
70 70 61 50 30
70 70 61 50 31
70 70 61 51 30
70 70 61 51 31
71 71 60 50 30
71 71 60 50 31
71 71 60 51 30
71 71 60 51 31
71 71 61 50 30
71 71 61 50 31
71 71 61 51 30
71 71 61 51 31

RG-15 70 70 70 70 70
71 71 71 71 71

 

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