Global shape with morphogen gradients and motile polarized cells

Steiner T, Trommler J, Brenn M, Jin Y, Sendhoff B. Global shape with morphogen gradients and motile polarized cells. In: 2009 IEEE Congress on Evolutionary Computation. IEEE; 2009: 2225-2232.A new cellular model for evolving stable, lightweight structures is presented in this paper. The focus lies in enhancing the ability of the cellular system to create complex 3D shapes with non self-similar regions. Compared to our previous work, the model proposed in this paper is composed of polarized cells that have directionally differential force functions for cell adhesion and thus are able to follow morphogen gradients (chemotaxis). We investigate the evolution of global information in form of evolving morphogen gradients that are created prior to development, which serve to guide cellular and shape differentiation. Our analysis shows that for a set of Pareto-optimal solutions of lightweight stable structures, no unique gradient can be evolved. Nevertheless, it is revealed that neighboring individuals in the genotype space are also neighbored in the gradient space. By contrast, neighborhood in the fitness space is not maintained in the genotype space. These results suggest that a hierarchical genetic formulation might be better than a 'common predefined spatial pattern' in form of a predefined gradient. In addition, our analysis also implies that some well-known properties in direct-coding evolutionary algorithms may be lost in developmental mappings