How to evolve the head-tail pattern from reaction-diffusion systems

The possible application of evolving artificial embryos to build functional machinery is a promising area of research. Unfortunately, there are still many fundamental problems to be solved before artificial embryology can be applied to such tasks, not to mention the necessary hardware. In this paper we address the problem of how to evolve the head-tail pattern for an artificial embryo endogenously, without predefined asymmetric cell division or external guide through polar cells or exogenous sources of morphogenes. We examine the performance of an evolutionary algorithm on two different fitness functions. Further, we examine the evolvability of several mathematical models for regulatory networks, controlling the behavior of the digital embryo.