  We present here a system of self-propelled particles that follow a very
simple motion law in continuous space in a deterministic and asynchronous way.
This system of particles is capable of producing, depending on the particle
density in the habitat, several spatio-temporal patterns emerging from an
initial randomized spatial configuration. We found that those structures show
specific population dynamics which arise from death (decay) and growth
(self-replication) of those structures, thus we call the system Primordial
Particle System (PPS), as the model can be interpreted as a simplistic model of
emergence of self-replicating chemical structures from initially chaotic mixed
components in the "primordial soup" at the beginning of life. We describe the
observed dynamics, show the emerging spatio-temporal structures and present a
macroscopic top-down model as well as a probabilistic microscopic bottom-up
model of the system.
