Environmental Engineering Reference
In-Depth Information
used discrete (stepwise) representations of space and time. Together with Stanislaw
Ulam, the work was developed at the Los Alamos Laboratory, where both were also
involved in the Manhattan Project.
1
Ulam used the idea to study crystallization
processes on a two-dimensional grid (or lattice). The first CA model that made the
approach widely known dated from the 1960s, when the Cambridge-based mathe-
matician John Conway developed the “Game of Life” (Gardner 1970). This is a
simple grid based process where cells can switch between two states following
simple rules (Sect.
8.3
). Because of its simplicity and surprisingly interesting and
complex behaviour, the Game of Life created a lasting enthusiasm.
During the 1970s, a series of applications of cellular automata models were
developed in physics to study gas and liquid diffusion, crystallization processes,
magnetic and spin phenomena (Forrester et al. 2007). CA were further used as step-
wise (discrete) approximation models for partial differential equations (see
Chap. 7).
During the 1980s, following a marked increase of computer availability and
computation power, the application of cellular automata has seen a significant
increase, especially in mathematics and physics. Scientists started to realize that a
discrete representation of systems could provide simpler and more efficient approx-
imations of spatially complex processes compared to continuous approximations.
It was then that cellular automata machines were constructed, in order to handle
parallel processing more efficiently (Toffoli and Margolus 1987). An important
contribution to CA was made by Wolfram (1994), who systematically explored the
overall dynamics of large classes of one-dimensional cellular automata using the
software “Mathematica”, which he developed initially for this purpose. Wolfram
showed that simple, deterministic rules can generate complex patterns in space or
time that look as if they were completely random. In ecology, CA successively
became one of the most frequently used approaches to model spatially extended
processes. Often, they are used in combination with other techniques such as
individual-based models (Chap. 12).
Due to their ease of implementation and capacity to simulate spatial patterns,
CAs have been widely applied to ecological problems related to spatial processes,
such as epidemic propagation (Sirakoulis et al. 2000), plant population dynamics
(e.g. Iwasa et al. 1991; Pascual et al. 2002), post-disturbance resilience (Matsinos
and Troumbis 2002), colonization processes (Silvertown et al. 1992; Hobbs and
Hobbs 1987), land-use and land-cover change (White et al. 1997) and spatial
competition of corals (Langmead and Sheppard 2004, see also Chap. 17). Rietkerk
et al. (2004) used a simple cellular automaton model based on the model of Thiery
et al. (1995) in order to understand how scale-dependent feedback can explain a
diversity of spatial patterns in self organizing savannah ecosystems. Moustakas
et al. (2006) developed a CA to analyse the interaction between fish schools and
fleets of fishing vessels, in order to assess the efficacy of conservation measures.
1
The Manhattan project covered the initial initiatives in the USA to develop nuclear weapons of
mass destruction. The leading physicists worked for this project during the Second World War.
