What is Cellular Automata?


Two simulations of growing towns-cities in CA. See both centers as “downtowns”. Each color is a representation of land use. Personal archives.
 
Cellular Automata (CA) was originally designed by Ulam and Von Neumann in the decade of the 40’s to provide an investigation model for complex systems behavior. Originally it was based on the inherent limitations of machines for their auto-reproduction. A CA system consists of a regular grid of cells, where each one of them could be in a number k of states, upgraded in synchronicity in lapses of time under interaction rules among the previous states of the neighboring cells. For example, the “Game of Life” of John Conway (1970) was based on a set of simple rules to study population’s space dynamics, where the cell had two states: alive (1) or dead (0) and three transition rules: survival, death and birth. With this simple system, extremely complex models are achieved; they grow – or they disappear – through a simulation. The rule (function) of growth or transition is contained in each cell in finite state that is translated in configurations of states of the “neighborhood.” (The cells, for established reasons die in some moment and/or they reproduce in contact with others).
The “neighborhood” consists of cells located around and adjacent of one given. For the models of one dimension the cells are connected with their neighboring r by each side; r is a parameter referred to the connection radius and it is expressed as 2r+1, including the cell itself.
CA shows the ability of a system to grow and then to alter its rhythm of growth, and possibly to revert it and die, what makes it essential in the simulation of biological populations’ behavior in a certain lapse of time.
In 1970, the first approaches to computarized models were applied to problems that demanded little information and, consequently little computer effort. Then, computers made possible the use of more information and the possibility to pass from models of big scale to microsimulation. The new techniques with the application of cellular Automata were introduced by Tobler (1979) to model geographical phenomena (Norte Pinto, Pais Antunes, 2007) based on the use of land. It is still discussed if the urban CA are evolutions of classic CA systems or if they are only models based on cells.
Since 1960 to middle ’80s, the interest was upon regional models. Then it became evident the necessity to understand the urban problems in small scale.
There are three classes of urban CA models, with different purposes (Norte Pinto, Pais Antunes, 2007):
a) models designated to explore the space complexity
b) models to investigate economic, sociological topics and of spatial complexity.
c) Models to produce operational tools of planning.
By middle ’80s, Helen Couclelis continues the investigation of CA applied to urban modelization, being this way two investigation lines established: the first related with complex systems and the second the possible uses in urban planning.
The transition rules among the “Game of Life” and the urban phenomena, are the following ones:
The “alive” cells are interpreted as urban areas – they could be clusters, blocks or isolated constructions – with a certain function. The cell continues alive if two or three neighboring cells have carried out their function, – birth, growth -.
The “dead” cells are those that have lost their urban function because four or more neighboring cells have carried out their function, – birth, growth – and they would suffocate the first one or, on the contrary, if only one neighboring cell is left over, the original one would die for its isolation.
The rebirth of the cell, takes place when there are three cells that comply exactly with their urban function. (A purpose to live). If none of the precedent conditions are met, the original cell stays dead.
Let us take into account some analogies:
The “death” of a town could be produced by these reasons among others:
Finalization of the main economic activity that gave it life.
Close of railroad stations.
Isolation caused by the layout of paved routes far from the old earth roads.
Lack of investment in improvement of existent routes.
Decrease in human population of each one of the involved communities, reflected in each census.
Weakness in their infrastructure of services due to town decreasing problem.
Lack of public transportations that allow the existent population’s transfer.
Lack of investment from the State in formal and informal education.
Lack of work sources.
Impossibility of information access and the opportunities in general.
Civil battles, wars.
Plague.
Kelso, California. Kelso originated as small collection of buildings along the Union Pacific Railroad in the Mojave desert. When the Second World War ended, the mine was closed and Kelso began to decline. As diesel engines replaced steam locomotives, trains no longer stopped for Kelso’s water. The station was closed in 1985 and in 1992, the Bureau of Land Management took over the property.http://www.ghosttown.info/ca/kelso/index.html
Another possible analogy is to take groups of different zonings (and in strict order) residential-industrial-commercial (White and Engelen, 1997). A cell in vacant state can change to the superior state, but the inverse action is not possible. We consider this not a very feasible situation; in Los Angeles and Orange County, for example, there are many similar situations of change of use but no area takes a “superior” state obligatorily. The changes will always be restricted by a general regulator plan in a master plan that includes all the areas of the city.
In the ’90s the non restriction concept is taken (unconstrained cells), where the characteristics of the cells are exclusively related with their state values, without interest in their location inside the grid; they are not restricted cells, for what the application of transition rules responds to the current configuration of cells. (White and Engelen, 1997).
In the years 2000 it is taken the concept of use of the land, that will depend on three factors:
The inherent qualities of land
The effects of the use of neighboring land
The aggregated level of demand for each use of land.
Finally, the innovation is the consideration of the fractal Dimension to verify the model behavior and the results of the urban simulation. Then, the fractal Dimensions are calculated for theoretical cities and compared with known fractal Dimension results of real cities.
I would advice in the output and input data. I took my time for my first exercise of CA in converting an urban block from La Boca, Buenos Aires, in a synthesis of cells. When I ran CA, with some selected conditions based on my experience on the real neighborhood, the resultant morphological pattern was completely different, but, to my surprise, the fractal dimension was pretty close to the one I got for the real pattern. So, the input was correct but the output did not reflect the urban situation. A couple of years after, using DUEM software, I designed two neighboring systems, I selected the conditions, including mixed use (residential, commercial and industrial) and I saw my two settlements growing until they conformed only one, after many iterations, both original “centers” (downtowns) were almost disappearing in the new pattern. This result was satisfactory for me, until I read the book “Collapse” by Jared Diamond and realized that some primary conditions for the extinction of a town or social group are highly difficult to represent in the softwares. This will be part of another post. My conclusion, CA simulations need a good group of interdisciplinary professionals analyzing the input and output data, it is not a game any more, it has to be based on real life situations.
Simulation in La Boca neighborhood, Buenos Aires. Personal archives.
The two towns-cities are growing, they are only one now, the two original centers are melting in the urban pattern. Personal archives.

REFERENCES
Couclelis, Helen : Geographic Illusion Systems: Towards a (Very Partial) Research Agenda for GIS in the Information Age
Norte Pinto, Nuno. Pais Antunes, Antonio. Cellular Autómata and Urban Studies: a Literary Survey. In Architecture, City and Environment. 2007
Norte Pinto, Nuno. Pais Antunes, Antonio. Modeling and Urban Studies: an Introduction. In Architecture, City and Environment. 2007
White R, Engelen G, “Cellular automata and fractal urban form: a cellular modelling approach to the evolution of urban land-use patterns” Environment and Planning A 25(8) 1175 – 1199. 1993
White, R., and G. Engelen. Cellular automata as the basis of integrated dynamic regional modelling. Environment and Planning B: Planning and Design 24, no. 2: 235-46. 1997.

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