To form complex symbolic expressions, the language of regular
expressions is convenient, whose operations are union, concatenation,
and iteration. Another operation which is sometimes useful is the
overlapping (whose symbol could be 
) of two strings; if the
words ax and yb each consist of letters a and b, joined to the
shorter words x and y, then:
(
is the empty word).
With such notation a symbolic de Bruijn matrix
could be defined; the symbolic form of the matrix shown above would be 0.30em
dots now represent the empty word. Such matrices would be multiplied by
using 
to multiply individual matrix elements. Subsequently
the advantage of substituting images --- such as the evolved cell ---
for the symbolic neighborhoods will be seen. The full neighborhood
matrix is rarely used, but it serves to illustrate very explicitly the
involvement of the row indices and the column indices with the individual
matrix elements.
