  This paper presents an application of the Infinite Unit Axiom, introduced by
Yaroslav Sergeyev, (see [11] - [14]) to the development of one-dimensional
cellular automata. This application allows the establishment of a new and more
precise metric on the space of definition for one-dimensional cellular
automata, whereby accuracy of computations is increased. Using this new metric,
open disks are defined and the number of points in each disk is computed. The
forward dynamics of a cellular automaton map are also studied via defined
equivalence classes. Using the Infinite Unit Axiom, the number of
configurations that stay close to a given configuration under the shift
automaton map can now be computed.
