Urban Growth Model with Cellular Automaton

Author: Candela Sol Pelliza

Introduction & Research Question

Cities are in constant development. More than 50% of the world’s population live in urban environments and the percentage keeps on growing. Cities in consequence too. City growing it’s a non-stoppable phenomenon that we should face as a society, and specially as urban planners. The question is not if cities are growing, it is how they grow, and what factors determines its development. Urban sprawl is a particular form of urban development that can be described as a complex multi-causal phenomenon, depending on various natural, social and administrative factors. These different aspects determine the way population density is distributed throughout the urban space and how fragmented the land is (OECD, 2018).

Mendoza is the 4th biggest city in Argentina. With a population bigger than 1 million inhabitants in its metropolitan region, and a geographic setting characterized by a dry climate and mountainous terrain, it is constantly facing the urban sprawl challenge. The most peripheral districts, which used to be rural areas, are the ones most affected nowadays, facing a fast development, with a lot of private housing projects moving towards de historically cultivation areas. Lujan de Cuyo is one of these districts.

Considering what was said before, the aim of this project is to understand which are the physical factors that have a major influence in the way the city is developing in the metropolitan area of Lujan de Cuyo, considering that this would be a key insight for a better territorial development planning. Therefore, the research question that will guide the simulation projects is the following:

What are the most influential physical factors in determining the characteristics of urban sprawl process in the metropolitan area of Lujan de Cuyo municipality?


a. Input data and Relevant Parameters

For the purposes of this model, only a fewphysicalinfluential aspects are going to be taken into account in order to simplify the experiment, being aware that for a more precise prediction, other elements such as urban codes and land prices should be also considered.

Following this logic, the evolution of the model is based on a composite parameter “Constructability”, which is, in turn, composed by the four main considered factors for the experiment, which are described below.

  • Distance to metropolitan city center: The main regional downtown, located in the central district of the province.

  • Distance to local city center: A local downtown, where the city of Lujan de Cuyo started developing, being an independent small district in its beginnings.

  • Distance to main roads: National and provincial routes and main highways and avenues in the area.

  • Distance to mountain area: It is considered as “mountain area” the zone that is specified as “mountain environmental reserve zone”, in which it is allowed to develop some housing projects, but with several restrictions.

Considering the described parameters, the input data should fulfil two purposes: in one hand, it should give the necessary information to model and analyse the previously described factors; in the other hand it must allow analysing the extension of the city in, at least, two different periods of times, in order to compare them, and be able to validate the model. Therefore, the following datasets are going to be used in the model:

  • Study area: Geojson file containing a polygon of the study area, which is the metropolitan zone of Mendoza (administratively defined as “Unicipio”), that is located inside Lujan de Cuyo Department.

  • Urban areas 2010: Geojson file containing the urbanized parts of the study area in the year 2010. This dataset is obtained from the provincial cadastral source.

  • Urban areas 2017: Geojson file containing the urbanized parts of the study area in the year 2010. The dataset is obtained from the provincial cadastral source

  • Main Roads: Geojson file containing the network of main roads in the study area.

  • Mountain Area: Geojson file containing the polygon that defines the boundaries of the mountainous zone, following the criteria previously described.

  • Lujan de Cuyo’s center: Geojson file containing the point of Lujan the Cuyo’s main square, which can be considered as the most central point of the downtown.

  • Mendoza’s center: Geojson file containing a line, which is the boundary of the study area in direction to the downtown.

Apart from the previous variables, the other constant parameter that is needed for establishing the way the model works is the “Built cells per step”. This establishes the speed of urban growing, setting how many cells are constructed in each step. The parameter is obtained based on real values, calculating the difference of built area between the official cadastral records of 2010 and 2017, and obtaining a monthly value of built area.

According to this, a total of 422Ha are built per year, meaning 35Ha per month. This value is converted to the working 2×2 Ha grid scale, obtaining a final value of 9 built cells per month, which is the «cycle» period considered in the model.

Figure 1. Model input Layers

b. Building the Model

The development of the model is based on the general assumption that the city grows in an expansive way, extending from the already urbanized areas and advancing to the vacant areas according to the previously described “Constructability” parameter.

Following the described logic, the general workflow consists of 3 main repeating steps: identifying the cells next to an already built cell (const_cells), calculating the constructability parameter for each one of these cells and sorting them descendingly, and urbanize the ones that have higher Constructability. The whole process workflow is detailed in the UML model in Figure 2.

To implement this in GAMA, the simulation is developed with a Cellular Automaton model based on a grid containing the urbanized and not urbanized areas in the year 2010. This grid is generated inside the model, as a «grid agent» based on the urbanized_2010_geosjson and study_area_geojson files, with a resolution of 2x2Ha. The other physical elements, such as the road network, the mountain area and the local and regional centre points, are modelled as species agents that interact with the grid for calculating the distances. Once the species and the grid are defined, the simulation workflow is defined through three main parts: the global initialization, the global reflex, and the grid section. The global initialization establishes the creation of the species, assigns values to the grid (1 for urbanized and 0 for not urbanized cells), and executes the normalize_distances() action, which makes the distances to the different species comparable.

The grid section contains the compute_distances() action which, based on the species location and the distance_to() built function, calculates the distance values from each cell. After that, a compute_constructability() action takes the already normalized distances and calculates the constructability parameter for the constructable cells (const_cells) each time step. Moreover, the section also contains a const{} reflex which is responsible for assigning, in each cycle, a true value to the const_bool boolean for the cells that are neighbouring a built cell.

The core function of the code is developed through a series of global reflexes: build{} creates a const_cell list containing on the cells neighbouring a built cell (the ones with const_bool=true), sorts them by their constructability, selects the 9 with the higher constructability value and «builds» them, assigning a grid_value=1. The reflex update_built_cells{} adds all the cells containing a grid_value=1 to the urban_cells list. Finally, the update_const_cells{} reflex, empties all the lists and returns the boolean variables to false for starting a new cycle.

c. Scenarios, Outputs and Validation

For obtaining results, the model is run, in the first stage, under 6 different combinations of parameters’ values. The combinations seek to analyse the model’s performance if the growth only depends on each one of the factors separately and if it depends on the four factors with the same weight.

The analysis of the results and validation of the model is achieved through two methods:

Visual Comparison: A visual-morpholical comparison between the predicted and the real urban expansion footprint. The main elements to take into account are the occupied area and the growing shape and directions.

Total urban footprint difference: The result of a symmetrical difference geoprocessing between the predicted urban footprint and the real one, for the whole study area, measured in Ha. The analysis of this indicator allows obtaining the percentage of «Correct predicted area» (cells predicted as urbanized in areas that are really urbanized) and «Incorrect predicted area» (cells predicted as urbanized in areas that are vacant in the reality)

The obtained results allow to clearly identify the most influential physical factors in the city growth process by analysing the accuracy of the results. In this sense, it is possible to affirm that the proximity to the main roads network is the main influential factor, followed by the proximity to Lujan de Cuyo local centre, Mendoza Center and finally, and almost with no influence, the proximity to the Mountain Area.

Having a better idea of how this individual factors affect the model, an additional sixth output is obtained as the result of calibrating the parameters according to the previously obtained values.

Conclussions and Discussion

After carrying out the complete process of project definition, workflow design, modelling and obtaining and validating results, it can be concluded that the model achieved the expected objectives, since it allowed answering the research question and obtaining new information about the phenomenon under study.

The model definition and development stage was extremely interesting and allowed learning about the system. It required the analysis of a complex phenomenon, such as urban growth, to understand its behaviour and to be able to model the intervening factors.

The results obtained allowed a deeper understanding of the elements that condition urban growth in the region of Luján de Cuyo. In this sense, some of the results correspond to what was expected according to the existing theoretical knowledge of the area, such as the preponderance of the factor of proximity to the main street network. However, others yield interesting new data, such as the clear preponderance of the factor of proximity to the regional center of Luján de Cuyo as opposed to proximity to the center of Mendoza.

Although the results obtained were satisfactory for a first approximation, the modelling process provided new perspectives on other elements that should be considered, such as street hierarchy, land value and accessibility.

In summary, it can be concluded that the project met the proposed objectives and provided a base model with great potential to be improved, extended and applied to different areas and objectives.

List of References

GAMA Platform. (2022). Retrieved from https://gama-platform.org/

Grignard, A., Taillandier, P., Gaudou, B., An Vo, D., Drogoul, A., & Quang, H. (2013). GAMA 1.6: Advancing the Art of Complex Agent-Based Modeling and Simulation. Pacific Rim International Conference on Multi-Agents (pp. 117-131). Dunedin, New Zeland: HAL.

Molina, J. E., Arboit, M. E., Maglione, D. S., Sedevich, A. y Mutani, G. (Noviembre 2019 – Abril 2020).

Estudio de expansión urbana, crecimiento poblacional, consumos energéticos e índices de vegetación

en el Área Metropolitana de Mendoza. AREA, 26(1), pp. 1-21. Retrieved from:


Molina, G.; Sedevich, A.; Suden, C.; Domizio, M. (2018). Contrapunto entre visiones complejas y acciones simplistas: el área metropolitana de Mendoza. VI Encuentro Latinoamericano de Metodología de las Ciencias Sociales, 7 al 9 de noviembre de 2018, Cuencua, Ecuador. EN: [Actas]. Ensenada : Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación. Centro Interdisciplinario de Metodología de las Ciencias Sociales. En Memoria Académica. Available at: http://www.memoria.fahce.unlp.edu.ar/trab_eventos/ev.12687/ev.12687.pdf

O’Sullivan, D., & Perry, G. L. (2013). Spatial Simulation: Exploring Pattern and Process. West Sussex: John Wiley & Sons.

Wallentin, G. (2022, December). UNIGIS module: Spatial Simulation. Retrieved from UNIGIS Salzburg: https://unigis-salzburg.github.io/Opt_Spatial-Simulation/

What are complex systems? (2022, December 13). Retrieved from Complex Systems Society: https://cssociety.org/about-us/what-are-cs

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