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their use of the FORTH language to represent their applications (because their text assumes the
reader has access to their customised parallel PC hardware extension CAM ), this topic is still the
clearest development of CA ideas to date. Wolfram's (1986, 1994) collections of papers also deal
with basic concepts but these are less applied. His topic in 2002 called A New Kind of Science is
a good summary of this point of view, but its relevance to cities and urban modelling is at pres-
ent remote. A particularly useful and broader rendition of the CA style of modelling is contained
in Resnick's (1994) wonderful little volume Termites, Turtles and Traffic Jams: Explorations in
Massively Parallel Micro-Worlds .
Agent-based simulations which build on CA have been developed in the field of artificial life. Many
papers of which have been published as part of the Santa Fe Series in Complexity, namely, the edited
volumes Artificial Life I, II, III and IV (Langton, 1989, 1994; Langton et al., 1991; Brooks and Maes,
1994). The topic by Epstein and Axtell (1996) Growing Artificial Societies: Social Science from the
Bottom Up provides a recent focus with strong implications for human geography. But the most com-
prehensive topic is that by O'Sullivan and Perry (2013), Spatial Simulation , which links CA to ABM
(Agent Based Modelling) in a way that is completely consistent with the ideas introduced here.
In urban modelling, the original papers by Tobler (1970, 1975, 1979) are worth studying as are
those by Couclelis (1985, 1988, 1989). The original application to Cincinnati and other US cities by
White and Engelen (1993) is important. We have noted that the topics by Marceau and Benenson
(2011) and the articles by Dragićević (2008, 2010) earlier are useful. In terms of generalising these
ideas to the wider science of cities, then Batty's (2005) Cities and Complexity is a good source, and
his recent topic (2013) The New Science of Cities shows where some of these ideas are heading.
How these all fit into GIS is provided in the text Geographic Information Systems and Science by
Longley et al. (2010). There are now many software packages relevant to this area, but by far, the
best is NetLogo (http://ccl.northwestern.edu/netlogo/) which is now a very general CA-ABM pack-
age with an excellent library of models and an urban suite (e.g. http://ccl.northwestern.edu/netlogo/
models/UrbanSuite-PositiveFeedback) based on Batty's (2005) topic.
REFERENCES
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Allen, P. M. 1982. Evolution, modelling and design in a complex world. Environment and Planning B 9:
95-111.
Axelrod, R. 1984. The Evolution of Cooperation . New York: Basic Books.
Batty, M. 1971. Modelling cities as dynamic systems. Nature 231: 425-428.
Batty, M. 1997. Cellular automata and urban form: A primer. Journal of the American Planning Association
63(2): 266-274.
Batty, M. 2005. Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models
and Fractals . Cambridge, MA: The MIT Press.
Batty, M. 2013. The New Science of Cities . Cambridge, MA: The MIT Press.
Batty, M. and Longley, P. 1986. The fractal simulation of urban structure. Environment and Planning A
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Batty, M. and Longley, P. A. 1994. Fractal Cities: A Geometry of Form and Function . London, U.K.:
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Batty, M. and Xie, Y. 1994. From cells to cities. Environment and Planning B 21: s31-s48.
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Modeling , eds. D. J. Maguire, M. Batty and M. F. Goodchild, pp. 151-172. Redlands, CA: ESRI Press.
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