Environmental Engineering Reference
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more complex; (iii) CA models can be modeled using generating
precise results (degree of closeness with real world systems); (iv)
CA can mimic the actions of any possible physical system; (v) CA
models are irreducible.
Conways's game of life, popularized by Gardner in 1970, was
pivotal in the promotion of these ideas through other fields of
science (Wolfram, 2002). Simulations of death and life in a game
showed the striking similarities between real life and simulated
life in a computer. Cells would survive or die in competition for
space, crowdedness, minimum number of neighbors required in
order to live in society, and reproduction. Emergent behavior,
not possible to justify directly by the input data, was one of the
topics of most curiosity among researchers.
In the field of urban and environmental planning, Waldo
Tobler, in contact with Arthur Burks, was exposed to Von
Neumann's works, and published ''Cellular geography'' (1979).
At NCGIA-Santa Barbara, Helen Couclelis and Keith Clarke,
published respectively ''Cellular worlds'' (Couclelis, 1985) and
develop the first fully operational and implementable CA (Clarke
and Gaydos, 1998). Michael Batty, initially at NCGIA-Buffalo
and afterwards at CASA-UCL, developed the theory and practice
that culminated in the publication of the seminal topics
Fractal
Cities
(Batty and Longley, 1994) and
Cities and Complexity
(Batty,
2005). Recently, Wolfram's topic
A New Kind of Science
(2002)
explores the importance of having a new science that does
not dismiss complexity, instead that tries to understand it and
apply it to a pan disciplinary development, that the geographic
information sciences obviously incorporate.
From there, links to fractals and bifurcations were an obvious
development as it became apparent that in some cases transition
was not constant and continuous, but the development of pat-
terns was less than randomized in time and space and some pat-
terns seemed to be repeating andmultiple time/space dimensions
(Silva, 2010a, Silva and Clarke 2002; Batty, Xie and Sun 1999).
As previously seen, starting with a smart-cell in a matrix
called a CA, it was now possible to identify/quantify processes
and patterns through computation, it was now possible to iden-
tify/quantify phase transitions, and detect emergent behaviour.
Anditwaspossibletodoallofthisnotonlyacrossspacein
a matrix of cells for a specific moment in time, but also along
systematic moments in time.
one wants to represent a physical world where humankind inter-
venes, it would be unreasonable to assume only a pure physical
(spatial) representation, and this means the need of including the
immaterial world (aspatial) in these new models and theories.
The challenge was to create a data structure that would allow that.
Therefore while CA developments were decisive to the under-
standing of complexity in spatial settings, at the same time (during
the 1940s and 1950s) a second branch of research was also being
developed that would be determinant to the development of
aspatial organization.
The founding fathers that are internationally recognized as
the ones contributing to the birth of the developments in mim-
icking the human decision-making process were: Albert W.
Tucker (1957, 1960) Merrill Flood and Melvin Dresher (RAND,
1952), and RAND's (www.rand.org) and Santa Fe Institute's
(www.santafe.edu) developments during the 1980s and 1990s.
One of the initial developments was linked with GA. In the
case of GAs, the goal was to focus on behavioral and social
systems. This second stream of research focuses on the different
behavioral options that human beings are faced with, using for
instance decision trees and neuronal nets, and extrapolating such
concepts to a new modeling environment called GAs.
While GAs usually do not have a direct representation in
space as it is the case with CA, they are very important as
representations of phenomena in terms of explaining what is at
the basis of decisions and options (i.e., why do we choose to
perform a specific option). Therefore GAs play a major role in
explaining decision-making processes that lead to specific spatial
actions. The core theory of GA is in the work developed by John
Nash exploring research results by Merrill Flood and Melvin
Dresher at RAND Corporation in the 1950s; in doing so he
opened up a new field of computational exploration of human
behaviour (Nash 1950, 1953).
The research developed by Flood and Dresher at RAND Cor-
poration are at the basis of the understanding of humanbehaviour
and how to extrapolate that behavior to understandable rules.
Their most known finding is ''the prisoner's dilemma:'' if two
prisoners (players) have a choice each on whether to betray the
other, and thus to decrease one's own jail time, while increasing
the jail time for the other, common sense tell us that in this com-
petitive environment a cooperative strategy should be the best
option; nevertheless, because of the uncertainty both will tend to
choose to ''betray.'' This leads to what is commonly known as a
''non-zero-sum game.'' The current set of strategy choices and
the corresponding payoffs constitute a sate of equilibrium (the
''Nash equilibrium'').
Consequently, human behavior could be classified according
to patterns in a more quantifiable way and Nash's equilibrium
represents the first clear demonstration of the outcome of self-
organization of agents accordingly to a set of new conditions.
Therefore, the post Second World War explanations of behavior
in a mathematical way, by attempting to incorporate the com-
plexity associated to individual behaviour, using game theory
and strategizing techniques, are at the basis of another impor-
tant element of theory by focusing on public-individual choice
and option.
One of the most common approaches towards the simulation
of the 'genetics' of human thinking is ABM. In contrast to CA's
abilities to model the spatial dynamics of land change, ABMs
proven to be most effective with aspatial dynamics. Advantages
of ABMs include their ability to model individual decision-
making entities and their interactions, to incorporate social
22.4
Agents: joining
with cells
If physical structures (spatial structures) and their (self) orga-
nization in the physical world at multiple scales and through
time could be measured computationally using CA. What about
immaterial structures (i.e., socioeconomic conductions), how are
they structured in order to produce an action? How do immate-
rial structures (aspatial structures) self-organize into meaningful
actions accordingly to a change in conditions?Why would imma-
terial structures and their organization be meaningful to physical
structures and to the material world?
Starting to answer the question: Why would immaterial struc-
tures be important to the material world? Because a thought is
capable of directing a physical action (i.e., command and control
of the brain that will activate movement in a hand). That is to
say that, while the physical world (without humankind's in the
equation) can be represented/explained by pixels and cells, if
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