The matrix elements of powers of the first stage matrix tell how many paths there are from the row index node to the column index node. Diagonal elements count loops. The trace counts all possible loops, once for each node which they contain, while specific diagonal elements identify the loops through that particular node.
Not all the possible loops will participate in the second stage matrix because they may not overlap correctly. The columns labelled ``initial'' contain the raw data, including transients as well as the ergodic set. Dropping all those nodes and links which lack predecessors, successors, or both, refines the data. In the process a new set of nodes and links may be exposed, which in turn ought to be dropped for a lack of continuation. Eventually, after ``gen'' cycles of iteration, zero, one, or more ergodic sets will be reached, in which there are no dead ends.
The ``final'' columns display the numbers of nodes and links in the second stage de Bruijn diagram, a separate line for each width. To a certain extent, these numbers can be divided by the width to get the number of symmetry classes. If very many of the patterns lack reflective symmetry, twice the width is an appropriate divisor; in any event the internal symmetry of the classes has to be taken into account.