  This paper introduces a continuous model for Multi-cellular Developmental
Design. The cells are fixed on a 2D grid and exchange "chemicals" with their
neighbors during the growth process. The quantity of chemicals that a cell
produces, as well as the differentiation value of the cell in the phenotype,
are controlled by a Neural Network (the genotype) that takes as inputs the
chemicals produced by the neighboring cells at the previous time step. In the
proposed model, the number of iterations of the growth process is not
pre-determined, but emerges during evolution: only organisms for which the
growth process stabilizes give a phenotype (the stable state), others are
declared nonviable. The optimization of the controller is done using the NEAT
algorithm, that optimizes both the topology and the weights of the Neural
Networks. Though each cell only receives local information from its neighbors,
the experimental results of the proposed approach on the 'flags' problems (the
phenotype must match a given 2D pattern) are almost as good as those of a
direct regression approach using the same model with global information.
Moreover, the resulting multi-cellular organisms exhibit almost perfect
self-healing characteristics.
