  Without loss of generalisation to other systems, including possibly
non-deterministic ones, we demonstrate the application of methods drawn from
algorithmic information dynamics to the characterisation and classification of
emergent and persistent patterns, motifs and colliding particles in Conway's
Game of Life (GoL), a cellular automaton serving as a case study illustrating
the way in which such ideas can be applied to a typical discrete dynamical
system. We explore the issue of local observations of closed systems whose
orbits may appear open because of inaccessibility to the global rules governing
the overall system. We also investigate aspects of symmetry related to
complexity in the distribution of patterns that occur with high frequency in
GoL (which we thus call motifs) and analyse the distribution of these motifs
with a view to tracking the changes in their algorithmic probability over time.
We demonstrate how the tools introduced are an alternative to other computable
measures that are unable to capture changes in emergent structures in evolving
complex systems that are often too small or too subtle to be properly
characterised by methods such as lossless compression and Shannon entropy.
