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calculate fractal dimensions easily using public domain data and
software like Fragstat.
Bolstered by new insights into the complexity of a geometric
kaleidoscope from the fractal perspective, both quantitative urban
modelers and qualitative urban social theorists have gained new
insights on urban spatial structure. For example, Sui and Wu
(2006) used lacunarity analysis - a new multiscale residential
segregation measure inspired by fractal geometry - to critically
re-examine the relative significance of class vs. race in shaping
the residential segregation patterns in a prismatic metropolis.
Social theorist Ed Soja (2000) chose the fractal dimension as
a metaphor to describe the restructured social mosaic in Los
Angeles. Fractal cities were used as one of the conceptual pillars
by Soja (2000) to characterize the ''metropolarities'' in what he
called the ''Post-metropolis.''
By introducing fractals into urban studies, we have gradu-
ally shifted from viewing cities as mosaics of geometric forms
as defined in Euclidean geometry to viewing cities as a recur-
sive world as described by the fractal geometry (Batty and
Hudson-Smith, 2007), echoing Berry's (1964) early synthesis of
''cities as systems within systems of cities.'' The significance of this
fundamental change in the spatial morphology tradition is still
unfolding. Undoubtedly, fractals have enabled urban researchers
to better understand the complex relationship between the parts
and the whole. Conceptually, fractals also imply unsettled com-
plexity and instability among the multiple social and spatial
relationships within cities, placing significant constraints on
confident generalization and accurate cartographic depiction as
classic urbanists have done.
built-in spatial interaction submodel to predict journey-to-work
and journey-to-shop flows. These types of models rely on the
implicit assumption that cities are like simple systems, usually
involving a finite number of individual elements. Consequently,
the entities in the models have to be aggregated to predefined
spatial units.
Although mounting criticisms in the 1970s (Lee, 1973; Sayer,
1976) of large-scale urban modeling approaches shook both
their foundation and practice, urban modeling efforts follow-
ing the social physics tradition in general and Lowry models in
particular did not die [perhaps Forrester's (1969) model is an
exception], but continued to evolve across several different con-
tinents (Wegener, 1994; Wegener and Furst, 1999). For instance,
modified versions of the Lowry models have been revitalized by
behavioral modifications through discrete choice models based
upon random utility theory (Anas, 1982; Wrigley and Longley,
1984; Ben-Akiva and Lerman, 1985; Roy and Thill, 2004), or
through their integration with GIS (Landis, 1995; Sui, 1998).
Instead of the crude predictions of spatial interaction modeling,
new models can predict choices between alternatives as function
of attributes of the alternatives, subject to stochastic dispersion
constraints taking account of unobserved attributes of the alter-
natives, such as differences in taste between decision makers and
uncertainty/lack of information.
In general, urban models following the social physics tradi-
tion tend to be aggregated, cross-sectional, and non-dynamic.
Gregory (1980) argued that the failure of this modeling tradition
''
...
is strategic: it allows for the uncontested mobilization of its
discursive element to secure the reproduction of specific struc-
tures of domination (p.341).'' Perhaps inspired by physicists'
dream of a final theory for the ultimate law of nature (Weinberg,
1994), Wilson (1995) also dreamed of a final theory in locational
analysis following the social physics tradition, but so far such a
final theory remains a dream. The urban modeling efforts fol-
lowing the social physics tradition have been stagnant/dormant
in recent years and seem to have been overtaken by the next
two traditions.
26.3.2
Cities as machines
-
the social
physics tradition
The social physics tradition of urban modeling concentrates on
studying mechanisms found in urban development. This tradi-
tion can be equated to Pepper's mechanism world hypothesis.
The driving metaphor of the social physics tradition has been
conceiving cities as machines, aiming to model interaction among
its different components, like the interactions between land use
and transportation. The large scale-models developed around
the mid-20th century can be classified as following this tradition
(Batty, 1976).
The application of basic laws from Newtonian physics to
social domains has a long history. They were earlier advocated
by Carey (1858), then applied in migration studies by Ravenstein
(1885) and in retail studies by Reilly (1931) and Lakshmanan
and Hansen (1965). After the principles of social physics were
proposed shortly after World War II (Stewart, 1947, 1950),
urban modelers have attempted to use all major concepts and
techniques developed in physics, such as entropy maximiza-
tion in statistical mechanics (Wilson, 1967), information theory
(Webber, 1979), synergetics (Haken, 1983), dissipative structure
(Straussfogel, 1991), self-organizing criticality (Bak, 1996), self-
organizing systems (Allen, 1997), small world/complex networks
(Urry, 2004), Brownian agents of active particles (Schweitzer and
Farmer, 2007), and even quantum physics (Arida, 2002). But
as far practical applications are concerned, the types of mod-
els developed by Lowry (1964) were perhaps those having the
biggest impacts. Essentially, the Lowry model is an aggregated
large-scale urban model based upon economic base theory with a
26.3.3
Cities as organisms
-
the
social biology tradition
The social biology tradition of urban modeling conceptualizes
cities as organisms. This tradition is related to Pepper's organism
world hypothesis, as it aims to understand how parts of the city (or
the city as a whole) grow/evolve. In contrast to the aggregated,
static, non-behavioral large-scale urban models following the
social physics tradition, models following the social biology tra-
dition tend to be disaggregated, dynamic, and more behaviorally
oriented, simulating patterns at the individual levels
2
.
Similar to the social physics tradition, conceiving cities as an
organism or some other biological entity has a long interdisci-
plinary history (Jacobs, 1961; Alexander, 1964; 2004; Steadman,
1979; Larkham, 1995; Khalil, 1998). Cities have been studied by
invoking ecological metaphors for understanding their resilience
(Pickett, Cadenasso, and Grove, 2004), metabolism metaphor for
exploring their internal material and energy flows (Olson, 1982),
cancer/epidemic metaphors for explaining urban systems growth
(Hern, 2008), or brain neural net metaphors for modeling traffic
networks within a city (Changizi and Destefano, 2009).
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