Wednesday, October 22, 2008

Design and implementation of an integrated GIS-based cellular automata model to characterize forest fire behaviour

S. Yassemi
a,S.Dragi ´ cevi ´ ca,∗
, M. Schmidtb
a Spatial Analysis and Modeling Laboratory, Department of Geography, Simon Fraser University, 8888 University Drive,
Burnaby, BC V5A 1S6, Canada
b Department of Geography, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada


The integration of geographic information systems (GIS) and environmental modelling has
been widely investigated for more than a decade. However, such integration has remained
a challenging task due to the temporal changes of environmental processes and the static
nature of GIS. This study integrates GIS and cellular automata (CA) techniques to develop
a fire behaviour model with a flexible and user-friendly end-user interface. The developed
model incorporates topographic, forest fuel and weather variables.

The performance of the implemented fire model is evaluated by comparison with fire spread simulations derived
from Prometheus, the national Canadian fire behaviour modelling tool based on elliptical
wave propagation principles. The developed fire behaviour model was tested using spatial
data from the 2001 Dogrib Fire near Nordegg Alberta, Canada. Results from the simulations
of the CA and wave propagation spread models indicate comparable agreement. This study
shows that the GIS-CAmodel can simulate realistic forest fire scenarios. The developed GIS-
basedmodelling tool enables dynamic animation within the GIS interface. Further, this tool
can be adapted to other CA-based spatio-temporal modelling applications.

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Saturday, October 11, 2008

A study on cellular automata based on relational databases and spatio-temporal simulations of culture diffusion

LUO Ping L2, DU Qing-yun 1, HE Su-fang 2, LI Sen 2, MICHAEL Gallaghel 3, NIU Hui-en 3
(1. School of Resources and Environmental Sciences, Wuhan University, Wuhan 430079, P. R. China; 2. Department of Tourism & Geography, Foshan University, Foshan 528000, P. R. China; 3. Shenzhen Graduate School of Town Planning, Shenzhen 518031, P. IL China)

ABSTRACT: This paper presents a development of the extended Cellular Automata (CA), based on relational databases
(RDB), to model dynamic interactions among spatial objects. The integration of Geographical Information System (GIS) and CA has the great advantage of simulating geographical processes. But standard CA has some restrictions in cellular
shape and neighbourhood and neighbour rules, which restrict the CA's ability to simulate complex, real world environments. This paper discusses a cell's spatial relation based on the spatial objeet's geometrical and non-geometrical characteris-
tics, and extends the cell' s neighbour definition, and considers that the cell' s neighbour lies in the forms of not only spatial adjacency but also attribute correlation. This paper then puts forward that spatial relations between two different cells can be divided into three types, ineluding spatial adjacency, neighbourhood and complicated separation. Based on traditional ideas, it is impossible to settle CA's restrictions completely. RDB-based CA is an academic experiment, in which
some fields are designed to describe the essential information needed to define and select a cell's neighbour.

The culture innovation diffusion system has multiple forms of space diffusion and inherited characteristics that the RDB-based CA is
capable of simulating more effectively. Finally this paper details a successful case study on the diffusion of fashion wear
trends. Compared to the original CA, the RDB-based CA is a more natural and efficient representation of human knowl-
edge over space, and is an effective tool in simulating complex systems that have multiple forms of spatial diffusion.
KEY WORDS: spatial relationship; cellular automata; relational database; culture diffusion; spatio-temporal simula-

The functionality of spatio-temporal analysis and modelling is a drive for GIS to further applications in various applied fields and digital earth plans. However, current commercial GIS lacks those capabilities for
spatio-temporal distribution, prediction, and simulation of spatio-temporal processes, and especially do not have the ability to simulate complex dynamic interactions among economic, human, cultural and ecological pro-
cesses(ZHANG and CUI, 2000). Thus, there is an urgent requirement for traditional GIS to provide not only spatio-temporal data management services but also tools for scenario generation. The basic thought to study

complex spatial system is to apply the theory of complex systems, combining the essential rules of geography, selecting proper study methods, and designing proper models. As a result, more effective and powerful methods for studying complex systems have begun to be
applied in order to understand geographic systems; for example, system dynamics, neural networks, artificial intelligence, etc. (ZHOU et al., 1999). The integration of GIS and dynamic models has become an important area of research on GIS because it greatly improves the ability
of GIS to support spatial decision-making and simulate geographical processes. The undamental problem, however, is that the conceptual representation of space and
time in dynamic modelling and in GIS are not com

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Using Cellular Automata for Integrated Modelling of Socio-environmental Systems

1) Guy Engelen , 2) Roger White , 1) Inge Uljee and 1) Paul Drazan
1) RIKS Research Institute for Knowledge Systems; P.O. Box 463; 6200 AL Maastricht; The Netherlands
2) Memorial University of Newfoundland; St. John’s; NF; Canada A1B 3X9

Cellular automata provide the key to a dynamic modelling and simulation framework that integrates socio-
economic with environmental models, and that operates at both micro and macro geographical scales. An
application to the problem of forecasting the effect of climate change on a small island state suggests that
such modelling techniques could help planners and policy makers design more effective policies --policies
better tuned both to specific local needs and to overall socio-economic and environmental constraints.

Town and country planners face the difficult task of dealing with a world that is complex, interconnected,
and ever-changing. Coastal zone management, urban land-use planning, and the design of policies for
sustainable economic development all pose the problem of dealing with systems in which natural and
human factors are thoroughly intertwined. There is growing scientific evidence that a purely macroscopic
approach to these problems does not suffice, because spatial and organizational details are important in
understanding the dynamics of such systems (Allen and Lesser, 1991; Kauffman, 1993; Langton, 1992;
Nicolis et al. 1989).
At the descriptive level, the need for spatial detail is attained in Geographical Information Systems. But,
in order to put forward effective measures for changing --or maintaining-- the organization of socio-
what is where why it is
economic and environmental systems, it is necessary not only to know but also
. These systems must be understood and managed as coherent dynamic entities, so that system
integrity is maintained. We present here a dynamic modelling framework and encompassing decision
support shell that is capable of integrating socio-economic and environmental factors at a variety of scales,
while representing spatial dynamics with a high level of geographical detail. This modelling framework is
quite general in terms of the situations to which it can be usefully applied. But we will present it here in
the form of an example --an application concerning the impact of climate change on a small island state.

An example: Exploring the Impact of Climate Change on a Small Island.
Shifting climate conditions, expressed at the in terms of changes in temperature,
precipitation, and storm frequency, are likely to affect productivity levels, demand patterns, and exports
and imports, and will probably cause migration of people and their activities as well (see e.g. Alm et al.,
1993). But all of these effects are actually expressed, on the ground, as phenomena. For
example, an increase in the total export demand for a particular agricultural product will normally mean
that more land will be required. But the consequences will be very different depending on whether the
land is found by converting existing agricultural land or by clearing forested land, especially if the latter is
easily eroded or is itself ecologically significant. Furthermore, changes in productivity that may occur as
other activities are displaced onto more marginal land, or as erosion causes loss of fertility, will in turn
have repercussions on the macro-level economics. In other words, the spatial details of land use are
important in understanding the impact of macro-level changes.
No one model is capable of capturing the whole range of these phenomena, from those operating on a
world scale down to those that threaten strips of beach or affect individual fields. For example, spatial
interaction based models, consisting of sets of linked dynamic equations, are useful for representing
spatial and temporal dynamics at regional scales (White, 1977; Engelen and Allen, 1986; Pumain et al.,
1989), but become computationally impractical when much spatial detail is required (White and Engelen,
1993). On the other hand, models capable of dealing with extreme geographical detail, such as those
available in Geographical Information Systems, lack the dynamics required to represent the processes
operating in the system (Brimicombe, 1993). One solution to the problem is to make use of a modelling
framework consisting of two linked components --one for macro-level processes and another for those
operating at the micro-level. Both components exchange results continuously during the simulation and
get the data relevant for their level of detail from the same geographical database, ideally a GIS (Figure
At the , the modelling framework integrates several component sub-models, representing the
natural, social, and economic sub-systems. These are all linked to each other in a network of mutual,
reciprocal, influence (Figure 1, top). The macro level allows for the use of regionalised representations
and for different types of mathematical formulations, thus permitting a more or less detailed modelling of
various aspects of the sub-systems as required for specific applications. For the case of the small
prototypical Caribbean Island, the macro-level is modelled as a single point in interaction with the world

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The application of a cellular automaton model for predicting deforestation: patterns and processes of LULCC in the Ecuadorian, Amazon

GIS/EM4 No. 92

Joseph P. Messina
Stephen J. Walsh


Global change research includes an extensive body of literature covering population-environment interactions focusing on the central issues of migration and demography, environmental site and situation, and socioeconomic structures addressed within a spatially-explicit but temporally dependent form. Quite often this is simply because neither the data nor the modeling methodology combine well to effectively address uncertainty and spatially defined time-series data within a nonlinear context. In this research, a cellular automaton model is proposed as an effective framework for the predictive modeling of landuse/landcover change (LULCC) associated with the spatial pattern and rates of deforestation and agricultural extensification in the Ecuadorian Amazon. The model employs user-defined rules based upon spatially explicit probabilities of LULCC derived from remotely sensed time-series data and both biophysical and socioeconomic regional characteristics to produce an output image of the "anthropomorphized" landscape over time and space.


Cellular automata, landscape dynamics, Amazon, deforestation, agricultural extensification, tropical forests, remote sensing, landscape dynamics

Environmental modeling often takes the approach that events are static in time and space. The more complex models, attempting to define process over time (e.g. GAP, GCM), rarely if ever include human activity as an integrated process. These human effects are difficult to model and do not follow the mechanistic forms favored by modelers. Further, attempts at mechanistic modeling of human activity have fallen from favor in the scientific literature. The process of land degradation, while in many cases visible to the eye and found throughout human history, has not been modeled to any significant degree (Blaikie and Brookfield, 1987). Redclift (1994) cites three primary flaws in the current paradigm used for the evaluation of LULCC processes: biological determinism, regionalization (fitting society into tight discrete social units for measure), and avoidance of time and space in the modeling process. In the context of the Ecuadorian Amazon, it is readily apparent that individual, social, and structural processes occur at different temporal and spatial scales and do so through feedbacks and thresholds within and across thematic, spatial, and temporal domains. Individuals can choose incorrectly, they may make decisions based upon the decisions of their neighbors or other units of social organization, or decide to satisfy the whims of a society far removed from their own. There are in fact many possible routes that an individual might take in making land use decisions. However, those decisions cluster around a common core. By defining the core decisions and modeling stochastically, it is possible to predict the majority of the decisions made by the regional community and their expression upon the landscape. Also, time-lags in landuse patterns associated with agricultural commodity prices or climatic trends and relationships to local and regional infrastructure affect LULCC decisions and spatio-temporal patterns expressed at the household level, the dominant proximate cause of deforestation in much of the Amazon basin. Within the Ecuadorian Amazon and much of Latin America, the nature of deforestation and farm creation may prove to be consistent enough to permit the development of deterministic models characterizing one or more of the landscape constituents. The changing temporal and spatial location/process of tropical development provides insight into the activities that currently encourage land clearing. In this way, spatial patterns point to a set of factors that can explain recent changes in regional rates of landuse/landcover change and provide focused spatial constructions suitable for modeling. While the output from the Oriente development model characterizes both the pattern and rate of regional deforestation, issues regarding comparative pattern analysis need to be addressed in complex or adaptive system terms.

The research study site in the northeastern Ecuadorian Amazon, known regionally as the Northern Oriente, is significant from a social, biophysical, and geographical basis. Settlers in the Napo and Sucumbios provinces are generally poor in-migrants settling on predefined 50 hectare plots, clearing primary forest to grow subsistence crops, coffee, and later, pasture for cattle (Whitaker 1990). The focus on the Ecuadorian Amazon is significant for environmental and socioeconomic reasons. The western Amazon region, bordering the Andes and lying at the headwaters of the Amazon River basin, possesses several major centers of endemism (Hiroaka and Yamamoto 1980). Despite its global biodiversity and carbon sequestration significance, agricultural settlement and concurrent deforestation threaten the region. The specific site selected for modeling is an intensive study area (ISA) of approximately 90,000 ha located to the northeast of the regional capital and largest central place, Lago Agrio. This area was selected for its rapid development and complex landscape variability (spatial pattern and compositional changes in landuse/landcover). Furthermore, this site serves as an on-going field site for study of forest reserve remnants. The Northern Oriente is also unique in that much of the morphology remains undefined within the literature. Regional elements have been overlooked in the Ecuadorian Amazonian due in part to the region's inaccessibility and in part to the lack of total area with respect to the much more politically popular and economically dominant Brazil. A major advantage of the Oriente over Brazilian rainforests lies in the scale dependent homogeneity of the climate, land surface, and social organization. It is this very homogeneity that supports meso-scale landscape diversity modeling as presented here.

Cellular automata
Cellular automata (CA) were originally conceived by Ulam and von Neumann in the 1940s to provide a formal framework for investigating the behavior of complex, extended systems (von Neumann 1966). Cellular automata are dynamic, discrete space and time systems. A cellular automaton system consists of a regular grid of cells, each of which can be in one of a finite number of k possible states, updated synchronously in discrete time steps according to a local, identical interaction rule. The state of a cell is determined by the previous states of a surrounding neighborhood of cells (Wolfram 1984). The infinite or finite cellular array (grid) is n-dimensional, where n=1,2,3 is used. The identical rule contained in each cell is essentially a finite state machine, usually specified in the form of a transition function or growth rule that addresses every possible neighborhood configuration of states. The neighborhood of a cell consists of the surrounding (adjacent) cells. For 1-D (one-dimensional) CA models, a cell is connected to r local neighbors (cells) on either side, where r is a parameter referred to as the radius (e.g. each cell has 2r+1 neighbors, including itself). The increasing application of cellular automata in general phenomenological modeling is an important indicator of the developmental potential of CA. The ability of a system to grow and then alter its rate of growth and possibly reverse or "die" is a fundamental goal in biological or human system CA modeling. Ermentrout and Edelstein-Keshet (1993) performed CA applications in biological modeling. The systems modeled by Clarke et al. (1996, 1997) and the example presented here both attempt to follow biological patterns of development. The difficulty in modeling population-environment interactions has historically been the necessary dual simulation mode of model construction. Human systems are necessarily stochastic while many natural systems are adequately modeled deterministically. Combining the two methodologically polar components into an effective approximation of reality requires the use of alternative modeling techniques.

Data and methods

Database development

The input data for the model include landuse/landcover layers derived using Landsat Thematic Mapper data from 1986 and 1996 and a 1973 Multi-Spectral Scanner scene rescaled and classified using a hybrid unsupervised/supervised classification scheme with the ERDAS Imagine software package (Messina et al 2000) (Figures 1,2). Class validation and accuracy assessments were performed using transformed divergence and random class fields. Field campaigns conducted in the spring of 1999 and 2000 provided geodetic and thematic control information. Additional data layers include roads digitized from 1:50,000 scale topographic maps, hydrography, elevation and slope from DTED 3 arc second data, as well as socioeconomic data collected at the household and community levels. Soils data are included but have not been tested for accuracy. These data are rescaled (1 bit to 2 byte) in order to optimize space and computing efficiency. Finally, social survey data collected via a 1990 probability sample of 480 farm households and repeated in 1999 for all sites were used in qualitative CA rule evaluation.

Figure 1 Figure 2

Figures 1, 2: 1986 and 1996 B5 Landsat Thematic Mapper Data - Intensive Study Sites in the Ecuadorian Amazon

Model development

The model employs the user-defined rules to produce an output image of the "anthropomorphized" landscape. In order to minimize data transform issues, the ERDAS Imagine Spatial Modeler, an interactive visual tool, was used for model development and implementation and enhanced through the use of the Spatial Modeler Language (SML). In order to better parameterize the image dynamics of the model, the individual growth rules were assembled and tested as discrete elements. Subsequent modeling efforts will be conducted using the IDL programming language as it supports multilevel modeling, integrated statistical tools, and is portable.

Random numbers

The first model component written creates a random number image. The random number generation procedure is vital to successful CA modeling. While CA purists will insist that only local neighborhood rules are necessary for CA modeling, the use of the stochastic component permits growth more closely mimicking reality. By design, the total number must be low, but the low number of random pixels selected necessitates an additive set of rules. In modeling the Oriente, the random number generator creates a random number field by selecting each pixel by row and column, and then applying a random number as a pixel digital number. This pixel digital number is then altered via an adjustable scalar value. The adjustability of the scalar value allows for iterative adjustments in increased or decreased growth rate conditions.

Growth rules

Organic growth spreads outward from existing urban centers and agricultural areas, representing the tendency of the humanized landscape to expand from social nodes of opportunity. Spontaneous growth occurs when a randomly chosen cell falls nearby an already urbanized cell, simulating the influence urban areas have on their surroundings (Clarke et al. 1997). Both organic and spontaneous growth rules are modeled in the first phase of the Oriente model. Focal filters are used to create a field of neighbor effect in order to approximate urban influence and allow the development to expand based upon the location of the random cell. By combining the two components into one section, the random effect is modeled as an additive component to the organic urbanization as a whole. Diffusive growth promotes the random dispersed development of agricultural plots regardless of proximity functions (Clarke et al. 1996). This type of growth component is handled later in the Oriente model with the second application of the random number field. In the Oriente model, the diffusion component is modeled using its own adjustable random number field and by modifying the organic growth routine by applying the focal filter using the maximum value criteria rather than the mean. Random dispersiveness is modeled by using a random number generator: identifying an intermediate image and applying a search function, or by applying a random number table to the focal filter to vary field characteristics. Random non-isotropic spreading is possible with the spreading center assignment acting randomly.

Road influenced growth, the most important driver of landscape alteration in the Oriente, encourages change cells to develop along the transportation network replicating the effects of increased accessibility. The likelihood of settlement and consequent deforestation along a road is high yet variable depending upon access to markets and settlement patterns. Road accessibility growth is currently modeled with another random number image, an adjustable search function, and an adjustable conditional statement. The model component outputs a "roadgrowth" image for visual validation. A corollary to road growth is river influenced growth. In many cases, the initial settlement push into a region is via river system transportation. As such, river growth is modeled using hydrographic information and the same routine as the road growth process. The physical element, slope, is iteratively applied as a categorized topographic relief variable. All the pixels at each step are analyzed with respect to the slope layer. This method seems unnecessarily repetitive, as the slope values themselves do not change, though the effect varies whereby slope constraints can and do change among growth rules. The Oriente model incorporates slope as a separate layer with an adjustable scalar function to modify the slope desirability over time as demand for land changes. In the final phases of model execution, excluded areas are removed, and the original urban extent image is added. It is inevitable that pixels will be incorrectly urbanized during the model run, as water areas and other types of features are not initially removed from consideration; therefore the excluded image is subtracted from the whole. Second, the original seed image is added back into the growth image to account for areas erroneously removed due to slope constraints and topographical data errors (Figure 3).

Figure 3

Figure 3: Oriente CA Model - excluding validation steps


Self-modification is necessary, as the model would otherwise produce linear or exponential growth (Clarke et al. 1997). The self-modification design element was included to better approximate the S-curve growth rate of urban and agricultural expansion; however, considering the artificial and non-rule based component of this implementation of self-modification, the resulting growth becomes temporally scale dependent. The self-modification criteria can be adjusted interactively; however, the annual iterative decrease is hard-coded. By limiting the areal extent of the region, the model is forced to retard growth to maintain equivalency in growth functionality. Over the course of multiple model runs, the boom and bust cycles likely cancel each other out, minimizing the effect. The agricultural versus urban growth modes vary according to both initial complexity and areal extent.


This initial calibration follows a comparative model of predicted versus actual change. The actual change is measured through the LULCC data sets created from the remotely sensed data. While the output from the Oriente model is certainly suitable for gross aspatial quantitative analysis, the spatially explicit output from this type of model may be analyzed using alternative techniques. With CA output data, the summary correlations by class tend to be more appropriate (Table 1). As the complexity of the seed image directly influences the shape and pace of growth, complexity may ultimately be the best measure of similarity (Messina et al. 2000). Most existing CA models, after multiple iteration, tend to produce smooth, isotropically consistent output. Standard measures of spatial autocorrelation are not used as they tend to provide false confidence in the results.

Total Area in Hectares Summary Correlations
- 1986 1996 Predicted 1996 actual Forested Urbanized Agriculture

Table 1. Total Area and Summary Correlations

Figure 4 Figure 5

Figures 4, 5: Predicted vs. Actual 1996 Landscape

Discussion and conclusions

Upon initial examination, the two images appear quite different (Figures 4,5). However, by comparing the model output with landuse/landcover data of the finest resolution, both the successes and the flaws of the model become apparent. The model predicts the total landscape change within the intensive study area region reasonably well with slight overprediction of agricultural expansion and slight underprediction of urban expansion. The summary correlations are lower than would be seen in a less complex environment due in part to the authors' intent in selecting a subset area of maximum spatial and quantitative change and in part to the diffusive growth limitations of the model. Specifically, the low urban correlation is due in large part to the effects of both roads (only one date of road coverage was used), random oil exploration activities, and the apparent change in social functions; the development of a service economy in and adjacent to market towns where household farms are being subdivided into relatively small parcels for residential development and secondarily the cultivation of commercial crops. The relative regional homogeneity of the biophysical, climatic regimes, and the importance of local farmers in deforestation as a response to the geographic accessibility to towns and the expanding transportation infrastructure permits the wider application of the model to multiple social and physical scales. However, one cannot avoid the fact that the spatial fit is less than ideal. The true measure of spatial complexity as applied in a CA context is one not yet fully realized in the literature and is like the next phase in this research. The tools exist to build complex (in the complicated not complexity sense) models to predict LULCC in a variety of environments and time periods. Without further development of the theoretical underpinnings of complexity theory and spatial pattern - what is a good fit - the models run the very real risk of over-specification. The Oriente, like most places, is surprisingly complex. As snapshots in time, images provide the raw material to assist in the derivation of complex environmental and human processes: in effect, to see patterns instead of isolated points and relationships between different distributions. The challenge of modeling population-environment interactions closely parallels the methodological concerns of much of social science. With improved data handling, the modeling scheme presented here is extensible to a variety of tropical environments and regional contexts, making cellular automata modeling not only a promoter of research into predictive spatial systems but more importantly an effective approach to modeling population-environment interactions across multiple spatial, temporal, and thematic domains. This work combines the historically descriptive aspects of society with remote sensing and landscape ecology towards the development of a Northern Oriente analogue. However, the challenges are many. None the least of which are (a) use of more suitable software for subsequent CA development, (b) integration of endogenous and exogenous factors in the model based upon the theories in human, political, and landscape ecology, (c) extension of the satellite time-series data for model development and calibration, (d) incorporation of time-lags and scale dependence of variables and their effects, (e) development of non-linear statistical tools better suited for CA systems, and (f) updated surfaces that represent proximate causes of deforestation and their hypothesized feedbacks across domains and thresholds of effects framed within a space-time context.

1. Portions of this paper were presented at the UCGIS 2000 Summer Assembly, Portland OR, June 23, 2000. See
References used

Blaikie, P. and Brookfield, H., 1987. Land Degradation and Society. Methuen, London.

Clarke, K.C., L. Gaydos, S. Hoppen, 1997. A Self-Modifying Cellular Automaton Model of Historical Urbanization in the San Francisco Bay Area, Environment and Planning B 24: 247-261.

Clarke, K.C., S. Hoppen, L. Gaydos, 1996. Methods and Techniques for Rigorous Calibration of a Cellular Automaton Model of Urban Growth. Third International Conference/Workshop on Integrating GIS and Environmental Modeling, Santa Fe, New Mexico, January 21-25, 1996. Santa Barbara: National Center for Geographic Information and Analysis.

Ermentrout G. B. and L. Edelstein-Keshet, 1993. Cellular Automata Approaches to Biological Modeling. Journal of Theoretical Biology 160:97-133.

Hiroaka, M, and S. Yamamoto. 1980. Agricultural Development in the Upper Amazon of Ecuador. Geographical Review 70{4}:423-446.

Messina, J.P., K.A. Crews-Meyer, and S.J. Walsh. 2000. Scale Dependent Pattern Metrics and Panel Data Analysis as Applied in a Multiphase Hybrid Landcover Classification Scheme. Proceedings of the 2000 ASPRS Conference.

Redclift, M. and Benton, T. (Editors), 1994. Social Theory and the Global Environment. Routledge, London, 271 pp.

von Neumann, J., 1966. Theory of Self-Reproducing Automata. Edited and completed by A.W. Burks. Illinois: University of Illinois Press.

Whitaker, M. D. 1990. The Human Factor and Agriculture. in Whitaker, M. D., and D. Colyer Eds. Agriculture and Economic Survival: The Role of Agriculture in Ecuador's Development. Westview Press Inc.

Wolfram, S., 1984. Cellular Automata as Models of Complexity. Nature 311:419-424.

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