Having succeeded in finding one single matrix for each automaton which
summarizes important properties of the distribution of its ancestors,
it is worthwhile examining some typical cases; because the matrices of
automata are unwieldy, it is convenient to make
the same points with
automata. We first consider an automaton
with a Garden of Eden and configurations with arbitrarily large numbers
of ancestors ( or), then one which has no Garden of Eden but which
is not reversible ( exclusive or), and finally one which is
reversible ( right shift). In due course we shall encounter
nontrivial reversible automata.