Measures of complexity for artificial embryogeny

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.

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