A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Complex Self-reproducing Systems

Abstract. Cellular automata and L-Systems are well-known formal models to describe the behaviour of biological processes. They are discrete dynamical systems, each of which can have complex and varied behaviour. Here, we study a class of substitutive systems incorporating properties of both cellular automata and L-systems, that exhibits self-reproducing behaviour. A one-dimensional array of cells is considered, each cell has a set of modes or states which are determined by a number from Z/nZ ∗ (n prime). The behaviour of a cell depends on the states of its neighbours and obeys to an additive rule. It has also a cell-division mode, which allows the line of cells to grow. The behaviour of such a model can be complex, but, using algebraic techniques, we prove that it can describe a reproducing system.