  In this paper we propose an approach for measuring growth of complexity of
emerging patterns in complex systems such as cellular automata. We discuss
several ways how a metric for measuring the complexity growth can be defined.
This includes approaches based on compression algorithms and artificial neural
networks. We believe such a metric can be useful for designing systems that
could exhibit open-ended evolution, which itself might be a prerequisite for
development of general artificial intelligence. We conduct experiments on 1D
and 2D grid worlds and demonstrate that using the proposed metric we can
automatically construct computational models with emerging properties similar
to those found in the Conway's Game of Life, as well as many other emergent
phenomena. Interestingly, some of the patterns we observe resemble forms of
artificial life. Our metric of structural complexity growth can be applied to a
wide range of complex systems, as it is not limited to cellular automata.
