Morphogenetic systems for resource bounded computation and modeling

A further exploration is presented of recent approaches to morphogenetic processes where geometry and form are fundamental primitives. Prior bottom-up approaches in morphogenetic modeling usually target a specific biological process aiming for optimal fidelity. We take a novel, more integrative and more abstract view of these phenomena and aim at properties such as (computational) universality, homeostasis, self-reproduction or self-healing, in both living and artificial evolving systems with explicit geometric 3D arrangements. We refine the recently introduced model of M systems (for morphogenetic systems) that leverages certain constructs in membrane computing and DNA self-assembly. The model is still based on local interactions of simple atomic components under explicit geometric constraints given by their shapes and spatial arrangements. We demonstrate two types of capabilities of the extended models. First, they are computationally universal in the Turing sense because they can simulate Turing machines very efficiently, with only a linear slowdown factor. Furthermore, they have the theoretical capability to probabilistically solve NP-hard problems in polynomial time. Second, more importantly, they unfold to exhibit certain macro-properties characteristic of living organisms (particularly, the ability of self-assembly of complex structures, self-reproduction and self-healing) as global properties observable at the macro-level, without explicit programming of these properties beyond simple rules of interaction. Besides providing a new theoretical background for this type of model, we provide quantitative evidence of these properties in a simple cell-like M system model. These results have been obtained using an M system simulator and visualizer that is available as open source software for further research in this area