From P systems to morphogenetic systems: an overview and open problems

Morphogenetic (M) systems are an abstract model of computation inspired by morphogenetic processes in living cells and organisms. They were created as a generalization of P systems with proteins on membranes. Abstract cells are not used as atomic elements but they can be assembled from simpler primitives called tiles with pre-defined shapes, sizes and changeable positions in 2D or 3D Euclidean space. This additional level of realism provides a closer relation to fields as synthetic or systems biology. We summarize known results on M systems which include studies of computational universality, computational efficiency in solving intractable problems, and we discuss their relation to other models of P systems. An important capability of M systems is their robustness under injuries and their self-healing properties which has been established theoretically and verified experimentally. Finally, we present results of computational experiments inspired by cell mitosis processes. All topics are accompanied with related open problems.