Pergamon
Comput., Environ. and Urban Systems, Vol. 22, No. 5, pp. 497±523, 1998
# 1998 Elsevier Science Ltd. All rights reserved
Printed in Great Britain
0198-9715/98 $19.00 + 0.00
PII: S0198-9715(98)00022-2
THE DIFFUSED CITY OF THE ITALIAN NORTH-EAST:
IDENTIFICATION OF URBAN DYNAMICS USING
CELLULAR AUTOMATA URBAN MODELS
Elena Besussi1,2, Arnaldo Cecchini 3 and Enrico Rinaldi 4
University of Venice, Institute of Architecture, Department of Social and
Economic Analysis of Territory, Stratema Laboratory, S.Croce 1957,
30135 Venice, Italy
ABSTRACT. The concept of ``diffused city'' refers to two hypotheses: that
changes in its physical and functional structure are essentially of urban type
displaying, for instance, processes of functional specialisation, or mobility which
is not commuting related; and that such changes are spatially distributed in a
diffused mode. This spatial organisation displays a multicentered and network
structure with ``softened'' functional hierarchies and it can be placed, with
regards to its quantitative (urbanisation's density) and qualitative (typology of
settled functions) features on the borderline between the ``city'' and the
``countryside''. In this research a family of cellular automata models is developed
in order to investigate such diffusion processes. The case study of the central area
of the Veneto region, the spatial organisation of which has inspired the concept of
diffused city, is presented together with some examples and the first results,
based on the application of a set of ``heuristic'' rules. # 1998 Elsevier Science
Ltd. All rights reserved
PURPOSES OF THE RESEARCH
In many ways a new urban dimension, which we could conventionally call ``postmodern'' with regards to its differences from the ``modern city'', seems to be emerging.
The modern city has acquired in time many unusual characteristics: it presents a mixture of
past and present, of permanencies and variations, of different functions (Castells, 1989;
Sassen, 1991). Thus it has been defined as a ``global city'' whose features are high density,
continuity and compactness, high living and housing costs, immigration and slums, service
branching, peripheral (or ``casual'') location of industrial areas, central location of
financial districts, diffusion of high-tech service industries, presence of low-level services
1
Corresponding author. Tel.: +39-41-2572156; fax: +39-41-5240403; e-mail: stratema@iuav.
unive.it
2
E-mail: [email protected]
3
E-mail: [email protected]
4
E-mail: [email protected]
497
498
E. Besussi et al.
industries, atypical job modes (``second jobs'', part-time, precarious self-employment,
moonlight jobs, etc.), large job opportunities, large unemployment, simultaneous effects of
diffusion and polarisation, presence of a spatial hierarchy. For the post-modern city we
have various definitions; among them, diffuse (or diffused) city,5 network city, networks of
cities, metropolitan ``lattice'', (world-wide, continental, national) urban lattice, interlatticed urban space, multipolar city, multiethnic city, productive city, fragmentary city,
``mashed'' city. We will investigate a particular urban phenomenon, which we have called
``diffused city'', focusing on its most relevant example in Italy, sited in the central area of
the Veneto region. The substantial indeterminacy shown by urban and regional
researchers, planners and policy makers6 when dealing with this area, is an obstacle to
the identification of its specific characteristics, evolutionary trends, emerging problems,
and to the building of a descriptive synthesis. This problem remains also in the
investigations about other similar metropolitan phenomena in Italy as the Puglia's coastal
urbanisation or the Marche's diffused industrial settlements. Beside this indeterminacy, it
is difficult to account for the different patterns of the contemporary city, due to diverging
``views of the worlds''. These interpretations are also related to different epistemological
formulations and to different ideologies or conceptions of the world (Sernini, 1988; this
paper).
We will try to reduce this indeterminacy following two paths. The first path reports the
theoretical frameworks, which have investigated, described and ``named'' this phenomenon. The purpose of this first step is to eliminate as many ambiguities as possible around
our choice to define what is and what should be identifiable as diffused city. The last steps
of this path collect descriptions and explanations provided by the different analytical
approaches about the relevance, role, origins and possible futures of this distinctive urban
region, and support the consistency of the choice of the case study. The second path
introduces the possibility to build a cellular automata (CA) model to describe the past and
on-going evolutionary dynamics of the diffused city which we have outlined: what we are
planning to obtain from this model is a consistency's evaluation of our hypotheses about
this phenomenon. The choice of CA to build urban models falls into a wider research on
new analytical tools, to overcome some theoretical and operational obstacles of large-scale
urban models (Batty, 1994; Klostermann, 1994; Lee, 1973, 1994). The theoretical
transcription and the empirical test will help us to identify the most significant variables
and relations between variables.
THE DIFFUSED CITY
Definitions: Noumena and Phenomena
The phenomenon is the same. The names change. Examining, however superficially,
preliminarily and partially the recent literature on the case study and, more generally, on
5
Notice that the combination ``diffused city'' is to be considered a neologism. Part of this research
proposes to validate the exactness of this terminology and to build formal references for its future
use.
6
In the past 25 years this area has been at the heart of the interests of local public planning
institutions in charge of building prescriptive tools for the management of urban growth and changes
and of research projects for the definition of descriptive and explanatory theories of such growth and
changes (Camicia, 1994).
The Diffused City and Cellular Automata Models
499
dispersed or nonconcentrated urban regions three different approaches have been
identified. They are loosely defined and often intersecting each other, yet they are clearly
distinct with regards to their theoretical references.
Urban Economy Perspective
This approach focuses on location factors of productive activities and residential
functions. Space is considered an external factor and described in terms of distances (and
infrastructures) affecting location choices. In these assumptions we find a strong reference
to location theories which integrate the spatial dimension into microeconomics (Sheppard,
1996). Classic location theory utilises microeconomics' concepts such as those of perfect
competition and perfect rationality but the over-simplified economic and spatial landscape
it assumes, is not sufficient to explain existing spatial processes where location choices
depend on relationships rather than on individual actor's choices. When trying to describe
regions characterised by diffused (industrial) settlements, urban economists has therefore
revisited for theoretical and operational purposes the concept (and terminology) of
``industrial districts'' (Goodman & Bamford, 1989). This is described as an industrial±
social±regional system (Becattini, 1989), a tight interlacement of people, knowledge, knowhow, firms and institutions. The presence/absence of these elements becomes the parameter
according to which urban systems can be described as diffused (Bagnasco, 1988; Fubini,
1994; Garofoli, 1991; Innocenti, 1985).
Socioeconomic Perspective
The key element of this approach is a conception of the city not as a physical object in
space but as a template, an ordering rule of spatial organisation. The city is the way
in which society is spatially organised in order to meet the requirements of the economic
system.7 This framework underlines the relevance of urban functions and of the effects of
their different spatial distributions according to which urban systems characterised by
strong rather than by weak functional hierarchies, by network structures rather than
by homogeneous and diffused growth, can emerge.8 The chosen case study has been
described as the outcome of the interactions between processes of urban deconcentration,
characterised by industrial facilities relocation and the diffusion of a manufacturing system
based on small firms, and the local social and cultural structure, characterised by small
dispersed rural settlements. These interactions gave rise to an archipelago's type of diffused
city (Bagnasco, 1994; Dematteis, 1992; Indovina, 1991; Petsimeris, 1989; Scaramellini,
1990, 1991).
Morphological Perspective
The focus is on the form of the city and on the distribution (level of dispersion/
compactness) of its physical elements only. Building typologies, urban and rural
landscapes, all the objects that can be observed at the intentionally small cartographic
scale of analysis, contribute at the identification of ``local environments''. Restricting the
7
This is also the assumption underlying the idea of an evolution from the ``modern'' to the ``postmodern'' city as a response to the evolution from a Fordist to a post-Fordist economic organisation
(Soya, 1995).
8
It is useful to remember that urban function is a polysemous and therefore equivocal concept, which
cannot be simply overlapped to that of the economic (or productive) sector. This is one of the main
differences with the urban economic approach. Cities are more than just marketplaces.
500
E. Besussi et al.
focus on physical objects of urban systems allows a less effective use of descriptive
categories as that of ``diffusion''. Therefore, if diffusion is a morphological typology, then
each dispersed settlement can be labelled diffused (Barbieri, 1996; Lanzani, 1991, 1996;
Secchi, 1996).
A Proposed Definition
In urban theories cities have been defined as the urban space unfolding, in compact
spatial patterns, from the effects of the interactions between social, economic and
institutional processes and existing physical elements. Yet the physical patterns of cities
has been changing leaving few clues for the understanding of urban dynamics. The link
between function and form seems broken. We believe that the chosen case study may
represents a particular case of new urban space characterised by a family of the following
parameters.
Density
All of the three analytical approaches reported in the first part of the paper refer to
dispersed settlements as an element of the diffused city. Therefore we assume that a low
level of density of land use is a required parameter for its identification. However we
cannot reasonably expect a low level of density to be homogeneously distributed over the
entire area, since this will contradict the urban quality of the phenomenon we want to
describe: therefore it is possible to assume that the mean value of density for the entire area
or for reasonably aggregated portions of that area, should remain within a fixed range of
values.
Urban Functions
The relevance of urban functions and of the effect of their different distributions in space
has been taken into account in the second analytical approach. Here we assume that a high
quantity and density of urban functions such as those typical of more compact cities (from
retailing of convenience goods to big wholesale centres, from household and local services
to large business ones) is able to trigger the evolution of a diffusely urbanised rural region
into a diffused city and the development of typical urban dynamics such as functional,
social, ``ecological'' specialisation. Therefore we consider high densities of urban functions
as a descriptive parameter of the diffused city.
Hierarchy
Even though it is reasonable to assume that the expulsion and relocation of population
which moved from historical and compact urban centres to the ``newly born'' diffused city,
importing urban type of collective demands, lifestyles and cultural patterns, actually
triggered this evolution, we are prone to believe in a future overturn of the functional
dependence between the compact and the diffused city. This organisational structure
would be a quite new type of spatial hierarchy. Therefore while the diffused city exhibits
weak inner hierarchies, it is probable that it will develop stronger hierarchies with other
urban systems, on a wider scale.
Mobility
A further parameter that can help to identify the diffused city is the mobility of
population, material goods, and information, within its area. To reinforce our hypothesis,
The Diffused City and Cellular Automata Models
501
according to which the urban character of this system is mostly identified by the way in
which the community ``uses'' its structural and spatial dimensions, high values of
mobility's variables would attest that the population moves within this area as it would do
in any compact city. Such variables should describe all trip's purposes (shopping, leisure
activities, wandering) not only the journeys to work or school (which are typical of
commuting basins only). An ultimate relevant consideration must be done: for many
different aspects we do NOT believe that the diffused city should be considered as a
passing phenomenon, a sort of ``transient form'', but that it is, however obviously
dynamic, a specific and autonomous organisation of urban space.
The Diffused City of the Central Area of Veneto: Geographical and
Morphological Aspects
The area comprised among the main urban centres (Figure 1) shows elements which we
have assumed as identifying the morphology of the diffused city. This area can be
described as a network with main nodes (large urban centres) and secondary nodes (small
and historical centres). Dispersed settlements have developed inside the meshes of this
network between the early 1970s and late 1980s, while more recently signs of
agglomeration along transport infrastructures have emerged. In short the morphological
elements of this area are:
(1)
(2)
(3)
large urban centres;
smaller centres;
welding between centres (Figure 2);
FIGURE 1. LandSat satellite image of the central area of the Veneto region (1990).
502
E. Besussi et al.
FIGURE 2. Weldings between small centres.
FIGURE 3. Minor linear growth.
(4)
(5)
growth of continuous urbanisation from the large centres either in the shape of
long and thin threads (Figure 3) or as wider settlements along new infrastructure
axes (Figure 4);
small, weak, yet thick networks, as the result of a filling-in type of growth among
the wider meshes of the network (Figure 5).
This area cannot be considered urban from a morphological point of view and it actually
lacks the continuity and density values of a more compact city. It is also important to
display data (Tables 1±3) describing the diffused city, which is the object of our
investigation, into the possible continuum, which goes from rural areas to the compact city.
RESEARCH TOOLS: CELLULAR AUTOMATA AND URBAN MODELS
CA have been introduced in the field of urban modelling when new theoretical
frameworks on urban evolutionary dynamics demanded for analytical tools and
techniques that could comprehend those theories. We are basically referring to the
The Diffused City and Cellular Automata Models
503
FIGURE 4. Growth on new transportation networks.
FIGURE 5. Growth on historical networks.
overcoming of strictly deterministic interpretations and to the disillusion for metaphorical/
descriptive models, which proved unable to account for urban dynamics in a predictive
perspective.
Urban and regional systems have been described as systems which evolve according to
nondeterministic dynamics, exhibit self-organisation, and where local interactions
establish global scenarios and account for the entire system's transformations. This
representation has increasingly become a new subject of investigation for urban analysis
(Besussi & Cecchini, 1997).
Given that CA support the possibility to build descriptive and, warily, predictive models
that can exploit such a representation and substantially contribute to restricting the field of
possible evolution alternatives, they seem a sufficiently proper technique to meet the
requests for analytical tools capable to reduce uncertainty on urban dynamics. These are
504
E. Besussi et al.
Table 1. Density of Employees
Chief towns
Torino
Milano
Venezia
Trieste
Genova
Bologna
Firenze
Perugia
Roma
Campobasso
Napoli
Bari
Reggio Calabria
Palermo
Cagliari
Province of Venice
Diffused City
Case Study Area
Turin Metropolitan
Area
Milan Metropolitan
Area
a
Area
(km2)
Total
employees
1981
Total
employees
1991
Growth (%)
1981±91
Density
(emp./k)m2
1981
Density
(emp./km2)
1991
130.17
181.74
457.47
84.46
238.84
140.73
102.41
449.92
1,507.6
55.65
117.27
116.14
236.02
117.27
133.51
2,460.18
1,284.46
97.97
744.12
475,225
818,188
151,250
90,646
280,537
205,509
185,556
51,410
885,958
17,469
316,629
117,457
37,184
177,251
70,955
270,198
372,982
15,089
687,990
422,020
756,281
137,664
845,27
239,509
205,674
195,979
41,398
951,018
19,474
321,068
121,510
41,398
173,534
82,894
287,722
399,438
19,810
640,123
711.2
77.6
79.0
76.8
714.6
0.0
5.6
719.5
7.3
11.5
1.4
3.5
11.3
72.1
16.8
6.5
7.1
31.3
77.0
3,650.8
4,502.0
330.6
1,073.2
1,174.6
1,460.3
1,811.9
114.3
587.7
313.9
2,700.0
1,011.3
157.5
1,511.5
531.5
109.8
217.0
167.3
461.6
3,242.1
4,161.3
300.9
1,000.8
1,002.8
1,461.5
1,913.7
92.0
630.8
349.9
2,737.9
1,046.2
175.4
1,479.8
620.9
117.0
264.7a
216.9a
467.1a
471.28
1,073,490
1,038,552
73.3
1,226.5
1,305.5a
Average density.
Table 2. Density of Population
Chief towns
Torino
Milano
Venezia
Trieste
Genova
Bologna
Firenze
Perugia
Roma
Campobasso
Napoli
Bari
Reggio Calabria
Palermo
Cagliari
Province of Venice
Diffuse City
Case Study Area
Turin Metropolitan
Area
Milan Metropolitan
Area
a
Average density.
Area
(km2)
Population
1981
Population
1991
130.17
181.74
457.47
84.46
238.84
140.73
102.41
449.92
1507.6
55.65
117.27
116.14
236.02
117.27
133.51
2,460.18
1,284.46
97.97
744.12
1,117,154
1,604,773
346,146
252,369
762,895
459,080
448,331
142,348
2,839,638
48,291
1,212,387
371,022
173,486
701,782
219,648
838,794
1,000,434
74,380
1,651,609
962,507
1,369,231
309,422
231,100
950,849
906,856
403,294
144,732
2,775,250
50,941
1,067,365
342,309
177,580
698,556
204,237
820,052
963,663
80,281
1,533,791
471.28
2,235,231
2,016,055
Growth (%)
1981±91
Density
(pop/km2)
1981
Density
(pop/km2)
1991
713.8
714.7
710.6
78.4
24.6
97.5
710.0
1.7
72.3
5.5
712.0
77.7
2.4
70.5
77.0
72.2
73.7
7.9
77.1
8582.3
8830.0
756.7
2988.0
3194.2
3262.1
4377.8
316.4
1883.5
867.8
10338.4
3194.6
735.0
5984.3
1645.2
356.5
654.3
880.5
1124.1
7394.2
7534.0
676.4
2736.2
3981.1
6443.9
3938.0
321.7
1840.8
915.4
9101.8
2947.4
752.4
5956.8
1529.8
371.4a
674.4a
946.7a
1164.1a
79.8
3101.2
3074.6a
The Diffused City and Cellular Automata Models
505
Table 3. Population Density for Different Areas in the Province of Venice
Area (km2)
Venice hinterland
Q1
Q14
Q16
Martellago*
Spinea*
20.09
15.03
Population 1991
16616
24514
Total
Average density
Density (pop/km2) 1991
841.0
1363.5
4868.0
827.1
1631.0
2172.4
Martellago*
Mirano*
Salzano*
Spinea*
20.09
45.66
17.19
15.03
16616
23994
9256
24514
Total
Average density
97.97
74380
Ceggia**
Torre di Mosto**
Santo Stino di Livenza**
22.0
38.3
68.1
5077
3739
11166
Total
Average density
128.5
19982
Cona**
Cavarzere**
64.7
140.3
3489
17753
Total
Average density
205.1
21242
827.1
525.5
538.5
1631.0
880.5
230.9
97.5
163.9
164.1
53.9
126.5
90.2
*Case study area; **rural areas.
the theoretical grounds of our choice. Beside them, in fact, the reasons, which have drawn
CA into the field of urban modelling, relate to the formal characteristics of these
techniques.
The historical disillusion (Lee, 1973) towards mathematical techniques for urban
analysis entailed a temporary abandoning of quantitative methods of analysis in favour of
qualitative ones. Such disillusion was not due to the limitations related to their
computational harshness which has been now overcome by the new information
technologies, but to the difficulties related with their use which made them inaccessible
to nontechnical operators.
CA provide the possibility to preserve both qualitative and quantitative approaches and
to combine them in a technical/mathematical structure which is also easy to process.
Morphological aspects can be displayed preserving their spatial organisation. The
transcription of an urban or regional system into a matrix of cells does not violate
the real spatial structure; indeed they overlap in a more or less neutral way, according
to the level of abstraction of the adopted semantic framework, whose choice always
pertains to the model's user. Urban phenomena can be described by means of local
interactions between individual cells since each of them has been initially attributed with a
specific ``state'' describing its meaning in the real system. These interactions must then be
506
E. Besussi et al.
translated into formal rules, which can be used by the cellular model, and again this
translation involves a semantic abstraction.
Shortly, this framework provides the possibility to describe urban and regional systems'
complexity (of form, function, and meaning), by means of a ``simple'' analytical
methodology, where local interactions based on spatial proximity underlie the system to
be investigated.
In this research, CA are specifically used to describe diffusive growth's processes, i.e.,
land-use transformation phenomena that ``percolate'' within a predefined system and
interact with its physical, functional and structural elements. Such phenomena can be
induced from outside the system itself (global scale as well as planning events), and
originate inside the system (long-term transformations, reaction processes activated when
specific variable values are met). Since the diffusion of such phenomena is considered to
happen by contact (meant in its broad sense of information transmission, Meier, 1962)
between elements, the use of CA seems suitable to describe and simulate these processes.
There are three types of applications and examples of CA (and of similar techniques) to
urban models' building:
(1)
(2)
(3)
They can build possible applications for submodels of specific urban and regional
dynamics such as traffic, land rent, pollution (Benati, 1997; Cecconi & Parisi, 1997;
Di Gregorio et al., 1997; Green, 1990; Nagel & Schreneckenberg, 1992) or provide
tools for models such as data and image processing models (Griguolo & Mazzanti,
1997; Miccoli, 1997). We could state, agreeing with Wegener (1994) that these are
mathematical urban models, not inclusive, operational.
They identify, from an abstract, theoretical or methodological perspective, possible
applications or frameworks (Batty & Xie, 1997; Cecchini, 1996; Cecchini & Viola,
1992; Couclelis, 1985; Longley & Batty, 1997; Papini & Rabino, 1997; Phipps &
Langlois, 1997; Takeyama, 1997; Wagner, 1997): these are mathematical (or
qualitative) urban models, inclusive, not operational.
They are real urban models combined with other modelling techniques (Clarke,
Hoppen, & Gaydos, 1997; White & Engelen, 1997): mathematical urban models,
inclusive and operational.
This research project concerns the building of an operational urban model combining at
different levels a set of CA models, which utilise only local interactions, and no other tool,
technique or model.
THE MODEL
Purposes
The fundamental hypothesis underlying this research is the possibility to build a genome
of the diffused city, assembling information from different case studies. In order to achieve
such a goal we must make a first step towards ``chromosomes'' identification, which can
only be achieved analysing the phenotypic elements (morphology, growth dynamics,
evolution) of the system. The research wants to points out the emergence of dynamic
patterns of identification (where and if existing) of the diffused city, overcoming the
classic description by way of morphological and structural patterns. The concept of
The Diffused City and Cellular Automata Models
507
dynamic pattern of identification refers to growth dynamics, which can be both
spontaneous, or a reaction to exceptional external events. Such dynamics should be
recognised as effective on a particular form of spatial organisation as well as on the entire
portion of space supporting such organisation.
A second purpose is to identify those factors, which are more likely to induce the
agglomeration or the dispersion of different functions and to understand which of these
functions are more or less exposed to hierarchisation's processes. We shouldn't forget,
however, that in this particular situation, a process of agglomeration does not linearly
determine an upward climbing of the hierarchical structures; hierarchies operate differently
according to the considered function (residential, industrial, commercial, leisure services,
etc.). This investigation supports the identification of possible competitions and/or cooperations among functions in growth and evolutionary dynamics.
A third purpose is the modelling of the flow of information, people, material and
immaterial goods, among different levels of density for the same function and, possibly,
among areas with similar density level. The goal of this analysis is the identification of
characteristic patterns of flows for the diffused city.
Description
Our hypothesis is that the diffused city is identified by a fixed set of values for certain
variables. Low values of residential housing's density; medium to high values of density for
commercial, manufacturing, service, social and cultural functions; high values of
``mobility'' between different functions and of purposeless mobility (wandering). Other
elements, which can be taken into account with regards to the definition of relevant
variables, are urban land values and housing typologies. The last, yet fundamental,
element is the strong character of self-similarity at different scales, which is particularly
significant for these types of cities (Batty & Longley, 1994).
For each of the assumed sets of variables (low density, medium to high density of urban
functions, high mobility) a possible spatial pattern of the diffused city can be defined.
Rules and cell states will be defined in the process of model building.
AuGe Ð The General Automaton for the Diffused City
If we recall the formerly proposed definition of diffused city, based on elements which
characterise density, functions and mobility (and, additionally, urban land value
distribution and self-similarity), we can conceive a General Automata Model for the
description and explanation of the diffused city (AuGe), based on the combination of
different structural automata.
The general automaton for the diffused city is designed as a set of modules and processes
(Figure 6) Ð basically specialised CA. Starting from an initial scenario, the aim is to
perform a simulation, which produces a final scenario able to display the evolution of an
urban area on the basis of the hypotheses and theoretical models of the diffused city. The
building of the initial scenario is performed by a module, which precedes the real model.
Through this module geographical, economic and social data of interest, previously stored
in a database are transformed into cellular information (cells of predefined states). The
initial scenario is the input of the first automata model, AuReS (land value transformation
automata); the output is a new scenario. This scenario is the input information for the
second automata model, AuFu, (urban functions' transformation automata); the output is
508
E. Besussi et al.
FIGURE 6. General automata for the diffused city. Scheme of the relations among data and procedures.
again a new scenario. The third scenario is then processed by the AuDi model (urban
functions' diffusion automata) which performs growth and decline of occupied cells. The
output of the model is another scenario.
At this stage two control modules verify the outcomes of the performed simulation:
functional density control module and morphological density control module. If the
test performed by the functional density control module gives a positive result the
outcomes are passed to the second module; if there is a negative result, the rules of
the AuFu model are modified. In the same way, if the test performed by the morphological
density control module has a positive result, the process moves on to the AuAu model
(self-similarity automata); if there's a negative result the rules of the AuDi model are
modified in the following iterations.
The Diffused City and Cellular Automata Models
509
The scenario processed by the last of the previous automata is then tested to verify that
each of its part satisfies the required criteria of self-similarity. The AuAu model performs
this test; if this test is successful, the last model, the mobility automata, is executed. If
the test is not successful, the simulation is run again Ð using this last scenario Ð from the
AuReS model. The last model, AuMo (mobility automata), performs the growth of
infrastructures (roads, etc.) according to functional and morphological and land-value
changes produced by the previous automata models.
AuGe can be organised on different spatial and temporal scales as shown in Table 4. In
this example for each iteration at Time 3 (which is equivalent to 5 ``real'' years), n (20)
iterations occur at Time 2; for each iteration at Time 2, there are k (100) iterations at Time
1; m (16) cells at Scale 1 represent 1 cell at Scale 2. Still following this example the AuMo
simulates ``trips'' among different functions and locations. After k iterations, it determines
the choice of a set of rules taken from all available rules of the AuFu which describes
change and development processes for ``urban functions'' and of the AuDi. These
automata run simultaneously and together with the AuReS, which controls the evolution
of land values (Cecchini, 1996), and the density control modules which supervise growth
dynamics. After n iterations of this quartet of automata, the model shifts to a higher
geographical scale: each association of states, composed of m cells, which belong to the
previously produced scenario, is associated with the state of a macro-cell. The AuAu is
applied to the level of macro-cells.
The Specialised Automata
It is opportune to describe in detail each of the modules, some of which are development
of specialised automata designed for different contexts (Cecchini, 1996). Rules will be
thoroughly described in the section on the implementation of AuGe.
AuReS (Land Values Automata)
This automaton (Figure 7) modifies land values' distribution and determines the
transition potentials of cells for the AuFu. Transition rules are based on hypotheses and
theories (gravitational, distance-decay) on causes and effects for land values modification.
Therefore AuReS set the scenarios for possible land use modification. These rules do not
provide for the growth of the total amount of occupied cells.
AuFu (Functional Automata)
As for AuReS, transition rules for this automaton are based on hypotheses on
interactions among urban functions and among different density levels for each function
(Figure 8). Rules do not provide for the growth of the total amount of ``active'' cells
Table 4. Logical Structure of the Model (AuGe): An Example
Scale 1
Mobility automaton (AuMo)
Scale 2
Time 1
Land values automaton (AuReS)
Functions automaton (AuFu)
Diffusion automaton (AuDi)
Morphological density control module
Functional density control module
Time 2
Self-similarity automaton
(AuAu)
Time 3
510
E. Besussi et al.
FIGURE 7. Scheme of AuReS processing.
FIGURE 8. Scheme of AuFu processing.
characterised by built elements. They define the distribution of urban functions and their
densities.
AuDi (Diffusion Automata)
This automaton simulates the diffusion of urban functions (Figure 9). Transition rules
are again based on hypotheses on growth dynamics of the diffused city. They provide for
the ``birth'' of new cells occupied by states characterised by built elements (housing,
industry, and commerce) and for the ``death'' of cells (disurbanization, abandonment).
Rules operate on all the cells of the scenario (both occupied and background cells).
The Diffused City and Cellular Automata Models
511
FIGURE 9. Scheme of AuDi processing.
FIGURE 10. Scheme of control modules.
Morphological density control. This module calculates density values in terms of
percentage of occupied cells over background (empty) cells for the entire investigated area
and for selected subareas. This module is activated in order to set a limit over
morphological density (i.e., to control concentration phenomena). When the calculated
density level reaches a fixed limit, the rules of the AuDi can be modified (Figure 10).
Functional density control. The number of cells for each function is ``weighted''
according to the density levels defined in the set of cell states (Figure 14). For instance,
512
E. Besussi et al.
cells belonging to the state residential-low density are multiplied by a 0.3 factor; cells of the
state housing-medium density are multiplied by 0.5; cells of the state housing-high density
by 1.0. In this case the weighted sum of 10 cells, 5 of which belong to low density, 2 to
medium density and 3 to high density would be (5*0.3)+(2*0.5)+(3*1.0)=5.5. This
operation is performed separately for each function. The obtained value is then compared
to predefined maximum and minimum threshold values. When the calculated value reaches
one of these thresholds, the rules of the AuFu can be modified (Figure 10).
AuAu Self-Similarity Control Module
This module verifies the presence (or absence) of self-similarity for each function (Figure
11). The area is parted in zones of decreasing sizes and densities' and settled urban
functions' values are calculated at different scales. If self-similarity is not supported, the
whole set of automata and modules is re-run, starting from AuReS.
AuMo Mobility Automaton
This automaton modifies the road network on the basis of existing relations between
groups of functions (Figure 12).
A FIRST IMPLEMENTATION OF AUGE
A preliminary version of the general automaton for the diffused city Ð consisting of a
subset of its modules Ð has been realised with the software interface Augh! (Rinaldi, 1998)
(Figure 13). The prototype has been applied to an area of approximately 10 km2 divided in
square cells of 30630 m.9
FIGURE 11. Scheme of AuAu processing.
9
Morphology data are derived from a raster transformation of digital vector maps (Besussi, 1998).
The Diffused City and Cellular Automata Models
513
FIGURE 12. Scheme of AuMo processing.
In this prototype, the spatial data processing is performed by a multi-automaton which
can be described as a chaining of different automata (AuReS, AuFu, AuDi) for which the
user can define the sets of states, rules, and the types of neighbourhoods. The scenario
resulting from the processing of the first automaton is used as an input for the following
one and so on until the last automaton in the chain. The final scenario is therefore the
outcome of the simulation performed with AuGe.
States of the Cells
The states of the cells for the automata activated in the prototype of AuGe are shown in
Figure 14.
Transition Rules
The rules defined for the three automata comprised in AuGe are here briefly described.
For a more detailed description see Appendix A.
AuReS Automata
Rules applied to value-marked cells. These rules support the typical behaviour of CA.
The cell modifies its state according to the states of the cells in the neighbourhood and to
its own state. They simulate the bias towards the homogenisation of land values in
different urban areas and the increase of values for residential areas due to the close
presence of commercial and service activities.
Group 1. A residential cell, marked with value x, surrounded by a number n (m of
residential cells marked with value y, tends to assume value y in a percentage of cases
p=f(m). For instance, if i is the total number of cells in the neighbourhood then p=(m/
i)6100.
514
E. Besussi et al.
FIGURE 13 Modules activated for the AuGe prototype.
Group 2. A residential cell marked with value x, surrounded by at least four
commercial/service±high-density cells, always assumes value (x+1).
Rules for decline and upgrading of residential cells. These rules describe processes of
``ageing'' of the residential real estates and upgrading interventions, which may raise the
value of single buildings.
Group 3. A percentage x of residential cells marked with value y assumes value (y71) at
each iteration.
Group 4. A percentage x of residential cells marked with value y assumes value (y+1)
at each iteration.
Group 5. A percentage x of residential cells marked with value y assumes value (y+2) at
each iteration.
The Diffused City and Cellular Automata Models
515
FIGURE 14. States of the cells.
Rules to simulate the affect of central areas. These rules describe the influence, even at
some distance, which central areas have on the value of the residential real estate.
Group 6. A residential cell marked with value y surrounded, within a radius of 2 cells, by
at least one cell representing a ``central area'' will assume the value (y+1) in a
percentage x of cases.
AuFu Automata
Rules for residential areas. These rules simulate agglomeration processes of residential
areas induced by the nearby presence of commercial and service activities.
(1)
(2)
Group 1. A residential±low-density cell surrounded by at least six commercial/
service±high-density cells, will assume the state ``residential±high density'' in a
percentage x of cases.
Group 2. A residential±low-density cell, surrounded by at least six commercial/
service±medium-density cells, will assume the state ``residential±medium-density''
in a percentage x of cases.
516
(3)
E. Besussi et al.
Group 3. A residential±low-density cell, surrounded by at least six commercial/
service±low-density cells, will assume the state ``residential±medium-density'' in a
percentage x of cases.
Rules for commercial and service areas. These rules simulate agglomeration processes of
commercial and service activities induced by the nearby presence of transport
infrastructures and of a high density of residential areas.
Group 4. A commercial/service±low-density cell, surrounded by at least four
residential±high/medium-density cells will assume the state ``commercial/service±high/
medium-density''.
AuDi Automata
Rules for the modification into empty land (background cells). These rules simulate the
``natural loss'' of very small commercial and service activities, of low value housing
independently of the surrounding environment. Besides they simulate the loss of industrial
activities due to processes of congestion or to the absence of infrastructures and services.
Group 1. A commercial/service±low-density cell will assume the ``background'' state in
x percent of cases.
Group 2. A residential±(any-density)±value-1 cell will assume the ``background'' state in
x percent of cases.
Group 3. An industrial cell surrounded by at least six industrial cells will assume the
``background'' state in a small percentage of cases.
Group 4. An industrial cell not surrounded by at least one infrastructures cell or one
industrial cell will assume the ``background'' state in a small percentage of cases.
Rules for the modification of empty land (background cells) into residential areas. These
rules simulate the diffusion of new low density and medium or high value housing, due to
the nearby presence of roads (linear growth) or of other low density housing
(agglomeration). These rules are controlled by a frequency of activation set to 10%.
This means that the rule will be applied only for the 10% of cases in which it should
actually be applied. This is to avoid processes of fast growth which do not belong to the
dynamics of the diffused city.
Group 5. A background cell surrounded by at least one infrastructures cell or by at least
six residential±low-density cells will assume the ``residential±low-density±(value-1 or
-2)'' state in 10% of cases.
Rules for the modification of empty land into industrial areas. This rule simulates the
growth of industrial areas induced by the nearby presence of other industrial areas and of
roads (processes of industrial co-operation).
Group 6. A background cell surrounded by at least one infrastructures cell and by at
least four industrial cells will assume the ``industrial'' state.
The Diffused City and Cellular Automata Models
FIGURE 15. (a) Initial scenario; (b) final scenario.
517
518
E. Besussi et al.
FIGURE 16. Outcomes after the execution of AuReS.
Rules for the modification of empty land into commercial/service areas. These rules
simulate the growth of commercial and service activities induced by the nearby presence of
medium and high density housings.
Group 7. A background cell surrounded by at least four residential±high-density±(anyvalue) cells will assume the ``commercial/service±medium/high-density'' state.
Group 8. A background cell surrounded by at least six residential±mediumdensity±(any-value) cells will assume the ``commercial/service±medium/high-density''
state.
Rules for the modification of empty land into public parks. This rule simulates the growth
of small public open spaces induced by the nearby presence of housings.
Group 9. A background cell completely surrounded by residential±(any-density)±(anyvalue) cells will assume the state ``public park'' in a small percentage of cases.
Application of AuGe to the Case-Study Area of the Veneto North-East
A single iteration of the sequence of automata (AuReS, AuFu, and AuDi) has been
processed, each iteration corresponding to an actual time span of 3±5 years. The outcomes
of the simulation are shown in Figure 15. The analysis of the outcomes of each automaton
provided a first testing of the reliability and significance of the whole set of rules. Therefore
The Diffused City and Cellular Automata Models
519
an early evaluation can be done. The application of AuReS has produced an overall
differentiation of land values, originally concentrated around the medium value (Figure
16). This change can be attributed to the simulated process of decline and upgrading,
which tends to either decrease or increase land values, and to that of values' diffusion.
The execution of AuFu has produced one single transformation, shown in detail in
Figure 17. These limited outcomes do not invalidate the set of rules as it is possible that
in following iterations, the other two automata will define different spatial distributions of
urban functions, more suitable for the application of AuFu.
Finally the execution of AuDi (Figure 15b) has produced a strong agglomeration
of residential areas along main roads and a limited loss of few cells representing low value
residential and industrial areas. On the whole AuGe is still going through a process of
calibration.
FIGURE 17. Details of the outcomes of AuFu: (a) before the execution of AuFu; (b) after the execution.
520
E. Besussi et al.
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APPENDIX A
A detailed description of the whole set of rules implemented for each automaton is
shown in Tables A1±A3.
Table A1. Rules of AuReS
Rule
no.
Cell
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
13
14
13
12
12
11
11
10
9
9
7
8
8
7
6
6
6
9
Neighborhood
[12,12,12,13,Q,Q,Q,Q]
[12,12,12,13,Q,Q,Q,Q]
[14,14,14,14,Q,Q,Q,Q]
[14,14,14,14,Q,Q,Q,Q]
[13,13,13,13,Q,Q,Q,Q]
[9,9,9,9,Q,Q,Q,Q]
[10,10,10,10,Q,Q,Q,Q]
[11,11,11,11,Q,Q,Q,Q]
[11,11,11,11,Q,Q,Q,Q]
[10,10,10,10,Q,Q,Q,Q]
[6,6,6,6,Q,Q,Q,Q]
[6,6,6,6,Q,Q,Q,Q]
[7,7,7,7,Q,Q,Q,Q]
[8,8,8,8,Q,Q,Q,Q]
[8,8,8,8,Q,Q,Q,Q]
[7,7,7,7,Q,Q,Q,Q]
[18,18,18,18,Q,Q,Q,Q]
[18,18,18,18,Q,Q,Q,Q]
NOT
Variations
conditions
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
12
12
14
14
13
9
10
11
11
10
6
6
7
8
8
7
7
10
f
p
Neighborhood
name
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
(Table continued overleaf)
522
E. Besussi et al.
Table A1. Continued
Rule
no.
Cell
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
12
7
10
13
7
8
10
11
14
12
13
9
10
6
7
6
9
12
6
38
7
39
9
40
10
41
12
42
13
Neighborhood
NOT
Variations
conditions
[18,18,18,18,Q,Q,Q,Q]
[18,18,18,18,Q,Q,Q,Q]
[18,18,18,18,Q,Q,Q,Q]
[18,18,18,18,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[5,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q]
[5,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q]
[5,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q]
[5,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q]
[5,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q]
[5,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q]
f
p
Neighborhood
name
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
13
8
11
14
6
7
9
10
13
13
14
10
11
7
8
8
11
14
7
100
100
100
100
2
2
2
2
2
2
2
2
2
2
2
2
2
2
5
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.1
AuReS-int.2
±
8
5
100
AuReS-int.2
±
10
5
100
AuReS-int.2
±
11
5
100
AuReS-int.2
±
13
5
100
AuReS-int.2
±
14
5
100
AuReS-int.2
f
p
Neighborhood
name
30
30
30
100
100
100
100
100
100
50
50
50
50
50
50
50
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
Table A2. Rules of AuFu
Rule Cell
no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
8
6
7
8
7
6
8
7
6
16
16
16
16
16
16
16
Neighborhood
[16,16,16,16,16,16,Q,Q]
[16,16,16,16,16,16,Q,Q]
[16,16,16,16,16,16,Q,Q]
[17,17,17,17,17,17,Q,Q]
[17,17,17,17,17,17,Q,Q]
[17,17,17,17,17,17,Q,Q]
[18,18,18,18,18,18,Q,Q]
[18,18,18,18,18,18,Q,Q]
[18,18,18,18,18,18,Q,Q]
[4,9,9,9,9,9,9,Q]
[10,10,10,10,10,10,4,Q]
[11,11,11,11,11,11,4,Q]
[12,12,12,12,12,12,4,Q]
[13,13,13,13,13,13,4,Q]
[14,14,14,14,14,14,4,Q]
[14,14,14,14,14,14,4,Q]
NOT
conditions
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
Variations
11
9
10
11
10
9
14
13
12
17
17
17
17
17
17
18
(Table continued on facing page)
The Diffused City and Cellular Automata Models
523
Table A2. Continued
Rule Cell
no.
17
18
19
20
21
16
16
16
16
16
Neighborhood
[13,13,13,13,13,13,4,Q]
[12,12,12,12,12,12,4,Q]
[11,11,11,11,11,11,4,Q]
[10,10,10,10,10,10,4,Q]
[4,9,9,9,9,9,9,Q]
NOT
conditions
Variations
±
±
±
±
±
18
18
18
18
18
f
p
Neighborhood
name
50
50
50
50
50
100
100
100
100
100
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
AuFu-int.1
Table A3. Rules of AuDi
Rule Cell
no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
15
15
1
1
1
1
1
1
1
1
1
1
1
1
1
15
15
12
9
6
16
1
1
1
1
1
1
1
1
Neighborhood
NOT
conditions
Variations
f
p
Neighborhood
name
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[9,9,9,9,9,9,Q,Q]
[10,10,10,10,10,10,Q,Q]
[11,11,11,11,11,11,Q,Q]
[11,11,11,11,11,11,Q,Q]
[10,10,10,10,10,10,Q,Q]
[9,9,9,9,9,9,Q,Q]
[15,15,15,15,4,Q,Q,Q]
[8,8,8,8,8,8,Q,Q]
[7,7,7,7,7,7,Q,Q]
[6,6,6,6,6,6,Q,Q]
[8,8,8,8,8,8,Q,Q]
[7,7,7,7,7,7,Q,Q]
[6,6,6,6,6,6,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[15,15,15,15,15,15,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[Q,Q,Q,Q,Q,Q,Q,Q]
[12,12,12,12,Q,Q,Q,Q]
[13,13,13,13,Q,Q,Q,Q]
[13,13,13,13,Q,Q,Q,Q]
[14,14,14,14,Q,Q,Q,Q]
[14,14,14,14,Q,Q,Q,Q]
[12,12,12,12,Q,Q,Q,Q]
[4,Q,Q,Q,Q,Q,Q,Q]
[4,Q,Q,Q,Q,Q,Q,Q]
[B,18,17,16,15,5,4,3,2,1]
±
[B,18,17,16,15,5,4,3,2,1]
±
±
±
±
±
±
±
±
±
±
±
±
±
[15,4]
±
±
±
±
±
±
±
±
±
±
±
±
±
3
1
1
18
18
18
17
17
17
15
8
8
8
7
7
7
1
1
1
1
1
1
17
18
17
18
17
18
7
8
100
100
100
50
50
50
50
50
50
100
100
100
100
100
100
100
100
100
100
100
100
100
50
50
50
50
50
50
100
100
5
5
5
100
100
100
100
100
100
100
100
100
100
100
100
100
5
5
5
5
5
5
100
100
100
100
100
100
5
5
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
AuDi-int.1
In the columns describing cells, neighborhoods, and variations, states are represented by
their ID number as in Figure 14. Q indicates that any state can be assumed by the cell.
NOT Conditions indicate which states are not included in the any state. Frequency refers to
the percentage of actual activation of the rule compared to the potential activation, while
probability to a random probability of activation. The neighborhood name indicates which
neighborhood is analyzed by the rule. Int.1 is a one cell radius neighborhood, while Int.2 is
a two cells radius.