Geoscience Reference
In-Depth Information
cooperative evolutionary game theory (Axelrod, 1984) has come from Michigan as did new devel-
opments of CA-like models in the fast-growing field of artificial life (Langton, 1989). Much of this
work has been quickly disseminated, linked to more general approaches to systems and complexity
theory and joined to new developments in morphology and non-linear dynamics such as fractal
geometry, chaos and bifurcation theory. The field itself has also been the subject of more funda-
mental theoretical explorations particularly by Wolfram (1984) who has classified CA in terms of
four varieties of system stability, and there have been various attempts to consider CA as parallel
computation (Toffoli and Margolus, 1987). Indeed, Wolfram (2002) in a remarkable and somewhat
speculative topic even goes as far as to state that the principles of CA represent
A New Kind of
Science
! Applications now abound in many fields which have a spatial bias and involve the evolu-
tion of populations, from ecology to astrophysics, but all are marked by a strong pedagogic flavour
(O'Sullivan and Perry, 2013). It would appear that CA are most useful in simplifying phenomena
to the point where the kernel of any local-global interaction is identified, and this has meant that
full-scale systems simulations based on CA are still rare, perhaps unlikely in that their charm and
attraction lie in their ability to reduce systems to their barest essentials.
2.4 NEIGHBOURHOODS, TRANSITIONS AND CONDITIONS
We will begin by examining the range of different CA that might be constructed by varying
neighbourhoods, transition rules, initial conditions and system states. Figure 2.2 illustrates four
different types of neighbourhood which are all based on the notion that the neighbourhood
(a)
(b)
(c)
(d)
FIGURE 2.2
Cellular neighbourhoods. (a) Moore. (b) von Neumann. (c) Extended von Neumann. (d) Non-
symmetric regular.
