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.
However, there are even greater similarities between the present work and that in @cite_5 . In both works, the grid is filled with cells at iteration 0 of the growth process (i.e. no replication is allowed) and chemicals are propagated only in a cell-cell fashion without the diffusion mechanisms used in @cite_8 @cite_2 . Indeed, a pure cell-cell communication is theoretically sufficient for modelling any kind of temporal diffusion function, since diffusion in the substrata is the result of successive transformation with non-linear functions (such as the ones implemented by sigmoidal neural networks with hidden neurons). However, this means that the optimization algorithm must tune both the diffusion reaction and the differentiation of the cells. On the other hand, whereas @cite_5 only consider the average of the chemical concentrations of the neighboring cells (i.e. is totalistic in the Cellular Automata terminology), our approach does take into account the topology of the organism at the controller level, de facto benefitting from orientation information. This results in a more general approach, though probably less efficient to reach symmetrical targets. Here again, further experiments must be run to give a solid answer.
@cite_5 @cite_2 @cite_8
2054742532 1546662014 1958651193
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.