Andrew Wuensche, Mike Lesser.
The Global Dynamics of Cellular Automata.
Addison Wesley. 1992
The Global Dynamics of Cellular Automata introduces a powerful new global perspective
for the study of discrete dynamical systems.
After first looking at the unique trajectory of a system’s future,
an algorithm is also presented that directly computes the multiple merging trajectories
that may have constituted the system’s past.
A given set of cellular automaton parameters will, in a sense,
crystallize state space into a set of basins of attraction
that will typically have the topology of branching trees rooted on attractor cycles.
The Global Dynamics of Cellular Automata makes accessible the explicit portraits
of these mathematical objects through computer-generated graphics.
The atlas presents a complete class of such objects, and is intended,
with the accompanying software, as an aid to navigation into the vast reaches of rule behavior space.
The Global Dynamics of Cellular Automata will appeal to students and researchers interested in cellular automata theory, complex systems, dynamical systems, computational theory, artificial life, neural networks, and aspects of genetics. The book contains work previously unpublished in scientific journals that may have profound significance in many areas of the sciences of complexity.