Jason Cawley
Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Posts: 712 
Those are outer totalistic rules. Basically, the totalistic scheme is applied for all cells except the center cell, but then duplicated for the two different cases, center cell = 0 and center cell = 1.
In the case of a 5 neighbor 2 color rule, that makes for 10 possible cases in the rule table.
outer total 4 and center cell 1
outer total 4 and center cell 0
outer total 3 and center cell 1
outer total 3 and center cell 0
outer total 2 and center cell 1
outer total 2 and center cell 0
outer total 1 and center cell 1
outer total 1 and center cell 0
outer total 0 and center cell 1
outer total 0 and center cell 0
Where "outer total" means the sum of the site values you have labeled b, d, f, and h.
The idea is to treat the rule number as having a "mixed base", with the "last digit" based on the center cell value and ranging from 0 to the number of colors minus 1, and the preceeding "digit"  of weight, number of colors, just as the second digit in standard arab numerals has weight 10  based on the outer total, with a value ranging from 0 to (neighborsize without center cell) * (colors 1).
When you use a full 9 neighbors, there are 18 cases in the rule table, from 9 possible outer totals (08) and 2 center cell values (0,1).
In Mathematica, the CellularAutomaton function takes a "kernel" argument in the rule portion, that specifies "weights" at different offsets. An outer totalistic rule can be specified by using a weight of 1 for the center cell, and a weight of k (number of colors) for all the others meant to be in the neighborhood. Thus 
{{0,2,0},{2,1,2},{0,2,0}}  as a table of weights, gives an outer totalistic 5 neighbor rule for 2 colors.
{{3,3,3},{3,1,3},{3,3,3}}  would give the weights for an outer totalistic 9 neighbor rule with 3 colors.
I hope this helps.
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