Figure 10: nominal ancestor screen
The number of ancestors of a configuration can be calculated with the help of matrices derived from the de Bruijn diagram. The row and column indices of these matrices are the partial neighborhoods of the automaton; therefore their dimension depends on the number of states and size of the neighborhood. for this reason, an LCAU program only contains the ancestor option when this combination is sufficiently small.
Unless a configuration is infinite, evolution always reduces its size; the missing information is provided by the indices of the de Bruijn matrix. Thus the row index describes the slightly larger left margin of the ancestral configuration, the column index describes the right margin. Periodic configurations depend only on the diagonal elements, those with quiescent support depend only on the element, q being the quiescent state.
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Harold V. McIntosh