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Without loss of generalisation to other systems, including possiblynon-deterministic ones, we demonstrate the application of methods drawn fromalgorithmic information dynamics to the characterisation and classification ofemergent and persistent patterns, motifs and colliding particles in Conway'sGame of Life (GoL), a cellular automaton serving as a case study illustratingthe way in which such ideas can be applied to a typical discrete dynamicalsystem. We explore the issue of local observations of closed systems whoseorbits may appear open because of inaccessibility to the global rules governingthe overall system. We also investigate aspects of symmetry related tocomplexity in the distribution of patterns that occur with high frequency inGoL (which we thus call motifs) and analyse the distribution of these motifswith a view to tracking the changes in their algorithmic probability over time.We demonstrate how the tools introduced are an alternative to other computablemeasures that are unable to capture changes in emergent structures in evolvingcomplex systems that are often too small or too subtle to be properlycharacterised by methods such as lossless compression and Shannon entropy.

Algorithmic Information Dynamics of Persistent Patterns and Colliding Particles in the Game of Life