  Modeling the immune system so that its essential functionalities stand out
without the need for every molecular or cellular interaction to be taken into
account has been challenging for many decades. Two competing approaches have
been the clonal selection theory and the idiotypic-network theory, each
stemming from a relatively separate set of principles. One recent perspective
holding the promise of unification is that of immunity as computation, that is,
of immunity as the process of computing the state of the body so that
protection can be effected, as well as boosted through learning. Here we
investigate the use of cellular automata (CA) as the core abstraction
supporting this new perspective. Our choice of CA for this role is based on the
potential variety of basins in a CA attractor field. Associating each basin
with a consistent set of body states, and moreover providing for the noisy
evolution of the CA in time so that jumping between basins is possible, have
provided the necessary backdrop. Given a CA rule to be followed by all cells
synchronously, our model is based on a probability with which each cell, at
each time step, independently updates its own state differently than the rule
mandates. Setting up and solving the corresponding Markov chain for its
stationary probabilities have revealed that already in the context of
elementary CA there exist rules that, while allowing transitions between
basins, display remarkable resiliency in terms of basin occupation. For these
rules, the long-run probability that the CA is found in a given basin is
practically the same as in the deterministic case when the initial CA state is
chosen uniformly at random. We argue that, consequently, our single-parameter
CA model may be a suitable abstraction of immunity as computation.
