Measuring Phenotypic Structural Complexity of Artificial Cellular Organisms - Approximation of Kolmogorov Complexity with Lempel-Ziv Compression

Artificial multi-cellular organisms develop from a single zygote to different structures and shapes, some simple, some complex. Such phenotypic structural complexity is the result of morphogenesis, where cells grow and differentiate according to the information encoded in the genome. In this paper we investigate the structural complexity of artificial cellular organisms at phenotypic level, in order to understand if genome information could be used to predict the emergent structural complexity. Our measure of structural complexity is based on the theory of Kolmogorov complexity and approximations. We relate the Lambda parameter, with its ability to detect different behavioral regimes, to the calculated structural complexity. It is shown that the easily computable Lempel-Ziv complexity approximation has a good ability to discriminate emergent structural complexity, thus providing a measurement that can be related to a genome parameter for estimation of the developed organism’s phenotypic complexity. The experimental model used herein is based on 1D, 2D and 3D Cellular Automata.