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.

Abstract. It has been suggested that evolving developmental programs instead of direct genotype-phenotype mappings may increase the scalability of Genetic Algorithms. Many of these Artificial Embryogeny (AE) models have been proposed and their evolutionary properties are being investigated. One of these properties concerns the fault-tolerance of at least a particular class of AE, which models the development of artificial multicellular organisms. It has been shown that such AE evolves designs capable of recovering phenotypic faults during development, even if faulttolerance is not selected for during evolution. This type of adaptivity is clearly very interesting both for theoretical reasons and possible robotic applications. In this paper we provide empirical evidence collected from a multicellular AE model showing a subtle relationship between evolution and development. These results explain why developmental fault-tolerance necessarily emerges during evolution. 1

Abstract. Echo State Networks (ESN) have demonstrated their efficiency in supervised learning of time series: a ”reservoir ” of neurons provide a set of dynamical systems that can be linearly combined to match the target dynamics, using a simple quadratic optimisation algorithm to tune the few free parameters. In an unsupervised learning context, however, another optimiser is needed. In this paper, an adaptive (1+1)-Evolution Strategy is used to optimise an ESN to tackle the ”flag ” problem, a classical benchmark from multi-cellular artificial embryogeny: the genotype is the cell controller of a Continuous Cellular Automata, and the phenotype, the image that corresponds to the fixedpoint of the resulting dynamical system, must match a given 2D pattern. This approach is able to provide excellent results with few evaluations, and favourably compares to that using the NEAT algorithm (a stateof-the-art neuro-evolution method) to evolve the cell controllers. Some characteristics of the fitness landscape of the ESN-based method are also investigated. 1

Artificial Embryogeny (AE) can be described as the use of a dynamical system as a mid-step in a design process; Through emulating Biological Embryogenesis, we hope to reach levels of complexity and robustness currently impossible. AE is a new field, and suffers from a lack of standards and meaningful means of evaluation. In this document, we review existing work, discussing motivations and merits of existing approaches. Throughout, we argue that a viewpoint which does not regard environment as a primary source of information risks taking a naive view of evolution. We argue that ``complexity'' is vaguely and inconsistently defined, and propose several novel measures; Perhaps the simplest model of AE, the Terminating Cellular Automaton, is introduced, and used to compute and contrast our measures. Next, the Deva family of AE algorithms is introduced, a modular Cellular Automaton-like group. A domain of application from Civil Engineering is chosen as an interpretation of the grown organisms. It is initially shown that it is possible to use a Deva algorithm to evolve Plane Trusses successfully, this interpretation providing a discipline-independent measure of success. A series of empirical experiments is undertaken, showing the relative efficacy and effects of several model-level strategies in the context of the evolution of structural design. Finally, we explore the role of environment as a constraint on development of structural form. We demonstrate a strong resistance to environmental change by successfully re-growing the organisms in new environments, showing that some Deva organisms are adding information from the environment to their overall morphology; This provides an arti?cial analogue to the re-use of genes which characterizes biological development.

We aim for a more rigorous discussion of “complexity ” for Artificial Embryogeny. Initially, we review several existing measures from Biology and Mathematics. We argue that measures which rank complexity through a Turing machine, or measures of information contained in a genome about an environment, are not desireable here; Instead, we argue for measures which provide the environment “for free”, allowing us to quantify the capacity for a genome to exploit a provided area of growth. This leads to our definition of Environmental Kolmogorov Complexity and Logical Depth, along with our introduction of novel measures of functional complexity. Next, we attempt at defining an exceptionally simple model of embryogenesis, the Terminating Cellular Automata. The described measures are computed in this context, and contrasted.