  The spatial Prisoner's Dilemma is a prototype model to show the emergence of
cooperation in very competitive environments. It considers players, at site of
lattices, that can either cooperate or defect when playing the Prisoner's
Dilemma with other z players. This model presents a rich phase diagram. Here we
consider players in cells of one-dimensional cellular automata. Each player
interacts with other z players. This geometry allows us to vary, in a simple
manner, the number of neighbors ranging from one up to the lattice size,
including self-interaction. This approach has multiple advantages. It is simple
to implement numerically and we are able to retrieve all the previous results
found in the previously considered lattices, with a faster convergence to
stationary values. More remarkable, it permits us to keep track of the
spatio-temporal evolution of each player of the automaton. Giving rise to
interesting patterns. These patterns allow the interpretation of
cooperation/defection clusters as particles, which can be absorbed and collided
among themselves. The presented approach represents a new paradigm to study the
emergence and maintenance of cooperation in the spatial Prisoner's Dilemma.
