## A (2,1) counterexample

Symbolic matrices can also be used to prove that a rule is

notinvertible; consider Rule 30 once more:0.45em

With little effort one can establish that

0.35em

for

n>1. Given that the configuration will always have some ancestors in which 1 remains 1 and others in which 0 becomes 1, there is no neighborhood length for which the ancestral cell is uniquely determined. Therefore Rule 30 cannot be reversed, in spite of the fact that every configuration has a unique ancestor whenever its external environment is specified.

Harold V. McIntosh

E-mail:mcintosh@servidor.unam.mx