Evolving cellular automata for form generation in artificial development

Form generation or morphogenesis has a crucial role in both artificial and natural development. This chapter presents results from simulations in which a genetic algorithm (GA) was used to evolve cellular automata (CA) in order to generate predefined 2D and 3D shapes. The 2D shapes initially considered were a square, a diamond, a triangle and a circle, whereas for the 3D case the shapes chosen were a cube and a sphere. The CA's rule was defined as a lookup table where the input was determined by the interaction neighborhood's cell state values, and the output established whether or not a cell was to be reproduced at the empty objective cell. Four different 2D interaction neighborhoods were considered: von Neumann, Moore, 2-Radial, and Margolus; a 3D Margolus neighborhood was used to generate the sphere and the cube. In all cases, the GA worked by evolving the chromosomes consisting of the CA rule table's output bits and a section of bits coding for the number of iterations that the model was to run. After the final chromosomes were obtained for all shapes, the CA model was allowed to run starting with a single cell in the middle of the lattice until the allowed number of iterations was reached and a shape was formed. The transition rules that formed some of these basic shapes and others were later combined with an Artificial (gene) Regulatory Network (ARN) to make up genomes that controlled the activation sequence of the CA's rules to generate predefined patterns. The ARN was also evolved by a GA in order to produce cell patterns through the selective activation and inhibition of genes. Morphogenetic gradients were used to provide cells with positional information that constrained cellular replication. After a genome was evolved, a single cell in the middle of the CA lattice was allowed to reproduce until a desired cell pattern consisting of the combination of basic forms was generated. © 2011 Nova Science Publishers, Inc