Population Dynamics of Self-Replicating Cell-like Structures Emerging from Chaos

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.