## Counting counterimages

Yet a third variation on the theme of symbolic de Bruijn matrices is actually a numerical matrix, whose purpose is to merely count counterimages, not to display them in some form. This final variant on Eq. 8,

gives an alternative definition of the de Bruijn matrix which in turn is decomposed into a sum

by defining

Still using Rule 22 as an example, 0.30em

Summing (rather than counting) the matrix elements again reveals seven counterimages.

Harold V. McIntosh

E-mail:mcintosh@servidor.unam.mx