The subset diagram which has just been discussed pertains to extending a partial neighborhood on the right, but an extension to the left could just as easily be made. Rule 22 is symmetric by reflection, but the partial neighborhoods are not, leaving the lefthanded subset matrix similar to the righthanded version by a permutation rearranging the subsets. For asymmetrical rules, such a similarity transformation would not exist.
0.3em
Since subsets of partial neighborhoods defining the rows are linked to those of the columns by incoming links, it would be more natural to use the transpose of the matrix shown to follow incoming links back through a configuration.