  John H. Conway's Game of Life, as well as cellular automata in the larger
family of Life-like CA, are discrete: the cells have a binary state space and
the birth and survival transition rules are 9-bits apiece. Inspired by Life,
several projects have developed continuously-valued cellular automata
frameworks in 2 dimensions. These CA systems are necessarily imperfect
approximations of ideal continuous systems when they are implemented in a
digital computer, and this inevitably leads to discretization errors. As we
know since at least the time of Poincair\'e's work on the three-body problem,
arbitrarily small errors in a complex dynamic system can lead to substantial
behavioral deviation over time.
  This outline of intent is based on observations in cellular automata that, in
certain cases, errors are not only well-tolerated, but are essential for
self-organization.
  This manuscript describes a set of experiments to investigate the importance
of discretization in approximating continuously valued dynamic systems, how and
when discretization is required for self-organization to occur, and the
relevance the results might have with respect to emergent agency and analogies
for consciousness.

Cellular Automata and Lattice Gases;Dynamical Systems