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.
The work by Gordon and Bentley @cite_5 differs from previous approaches by considering only communication and differentiation in the substrata. The grid starts with a cell at all available grid points, and cells communicate by diffusing chemicals to neighboring cells only. Each cell then receives as input one chemical concentration, computed as the average of the concentrations of all neighboring cells: hence, no orientation information is available. In the Cellular Automata context, such system is called a totalistic automaton. One drawback of this approach is that it requires that some cells have different chemicals concentration at start-up. Furthermore, it makes the whole model biased toward symmetrical patterns ("four-fold dihedral symmetry"). The controller is a set of 20 rules that produce one of the four chemicals and sends it towards neighboring cells. The set of rules is represented by a bit vector and is evolved using a classical bitstring GA. The paper ends with some comparisons with previous works, namely @cite_8 @cite_2 , demonstrating comparable and sometimes better results. But a possible explanation for that success could be the above-mentionned bias of the method toward symmetrical patterns.
@cite_5 @cite_2 @cite_8
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Today's software is brittle. A tiny corruption in an executable will normally result in terminal failure of that program. But nature does not seem to suffer from the same problems. A multicellular organism, its genes evolved and developed, shows graceful degradation: should it be damaged, it is designed to continue to work. This paper describes an investigation into software with the same properties. Three programs, one human-designed, one evolved using genetic programming, and one evolved and developed using a fractal developmental system are compared. All three calculate the square root of a number. The programs are damaged by corrupting their compiled executable code, and the ability for each of them to survive such damage is assessed. Experiments demonstrate that only the evolutionary developmental code shows graceful degradation after damage. A method for evolving programs that construct multicellular structures (organisms) is described. The paper concentrates on the difficult problem of evolving a cell program that constructs a fixed size French flag. We obtain and analyze an organism that shows a remarkable ability to repair itself when subjected to severe damage. Its behaviour resembles the regenerative power of some living organisms.