#Conways game of life heat map full#

Thus, we claim that our PPS represents the simplest model capable of predicting the emergence of ordered structures that behave, interact, grow, heal, replicate, and die without showing high sensitivity on parameters (particle connectivity, speed, density), as we show by our results. Unlike other simplistic models, most prominently Conway’s “Game of Life” 16, PPS produce natural-like structures (cells, spores) and dynamics (emergent ecology, emergent life cycles) without any restriction to unnatural modeling constraints like spatial discretization or time synchronization of agents. In contrast to existing protocell models 12, 15 PPS are significantly simpler without impairing their dynamics, thus they are more general and fundamental. We named this class of systems “Primordial Particle Systems” (PPS), as they model a spontaneous emergence of life-like structures.

Thus we consider those structures to be protocells 12 as they encapsulate the basic properties of very early life forms in the primordial soup 13, 14. These structures show distinct lifecycles with morphogenesis and reproduction.

We discovered a simple motion law for self-propelled particles (SPP) 11 allowing spontaneous emergence of self-sustaining and self-reproducing protocells 12 from populations of homogeneous reactive particles. No general simple proximate model yields such dynamic complex structures, and it is undecided whether there was “gene first” or “metabolism (cell) first” 9, 10 at the origin of life. These structures reside at equilibrium of growth and decay, in which unordered particles are self-ordering and - after some time - fall back to unorderedness 1, 7, as living systems manage to reside far from a thermodynamic equilibrium 8.

#Conways game of life heat map full#

Key singularities, in which order emerges and self-sustains from chaotic substrates, still wait for full understanding 2: Our universe is self-structuring, self-replicating life-forms emerged from simple molecules and simple chemical interaction patterns produce persistent complex thoughts in our brains 3, 4, 5, 6. The emergence of order from chaos is one of the key phenomena in morphogenesis across spatiotemporal scales 1. The generality and simplicity of the motion law provokes the thought that one fundamental rule, described by one simple equation yields various structures in nature: it may work on different time- and size scales, ranging from the self-structuring universe, to emergence of living beings, down to the emergent subatomic formation of matter. Finally, we explore parameter space for potential other candidates of life. Basic properties of the emerging structures (size distributions, longevity) are analyzed as well as their resilience against sensor or actuation noise. Here we analyze the macroscopic properties of the emerging ecology, as well as the microscopic properties of the mechanism that leads to it. These structures grow and reproduce on their own, show self-driven behavior and interact with each other. The emergent cells we found show a distinct life cycle and even create their own ecosystem from scratch. The patterns emerging within this system resemble patterns found in living organisms. We discovered a simple motion law for moving and interacting self-propelled particles leading to a self-structuring, self-reproducing and self-sustaining life-like system. Self-structuring patterns can be observed all over the universe, from galaxies to molecules to living matter, yet their emergence is waiting for full understanding.