  We consider transformations between attractor basins of binary cylindrical
cellular automata resulting from mutations. A t-point mutation of a state
consists in toggling t sites in that state. Results of such mutations are
described by a rule-dependent probability matrix. The structure of this matrix
is studied in relation to the structure of the state transition diagram and
several theorems relating these are proved for the case of additive rules. It
is shown that the steady state of the Markov process defined by the probability
matrix is always the uniform distribution over the state transition diagram.
Some results on eigenvalues are also obtained.
