Cellular Automata

Cellular automata are a class of abstract models that exhibit complex spatial dynamics. Cellular automata[Page 30] are attractive as relatively simple representations of apparently complex processes. In human geography, cellular automata have been used to model urban development and sprawl, land use and land cover change, and the spatial interactions of social groups.

In computer science, an automaton is a machine whose internal state changes in response to its current state and the state of its inputs. A cellular automaton (CA) is a collection of identical automata interconnected in a lattice or an array, so that the inputs to each automaton are the states of neighboring automata. Each automaton is a cell whose evolution is governed by its current state and by the changing states of neighboring cells. In geographic applications, two-dimensional grid arrays with each cell connected to its four or eight immediate neighbors are most common, although other array configurations are possible. The mapping that defines how each combination of the current and neighboring states of a cell leads to the next state is termed a rule. A rule may be deterministic or stochastic, and cell state changes may occur simultaneously for all cells or sequentially.

This description gives little sense of the variety of dynamic behavior exhibited by cellular automata. John Conway's “Game of Life” generates patterns reminiscent of the development of cell cultures on a microscope slide from a very simple rule and is the best-known example, with many free implementations available on-line. In general, there is no way to predict the global behavior of a cellular automaton from the rule governing its behavior at the local cellular level. This characteristic resonates strongly with the issue of understanding how processes scale up and down in geography.

In human geography and planning, CAs have served both as simple abstract models and as the basis for more complicated models of urban development and sprawl, land use and land cover change, and the spatial interaction of social groups. Consider, for example, how land use and land cover change can be represented in a CA. Using remote-sensed imagery, land cover classification may be assigned to every cell on a map grid. Possible and likely transitions in land cover classes can be described as a rule, so that land cover dynamics are represented by the evolution of a CA. For example, land classified as “industrial” might change to “derelict” but not immediately to “park-land.” A simpler example might use only two cell states, developed and not developed, to explore urban growth and sprawl.

Models along these lines have been presented by Michael Batty, Keith Clarke, and Roger White, among others. Many departures from the standard CA architecture are typical in geographic applications. In particular, geographers have been concerned with accommodating nonlocal interaction between cells and have experimented with cell update sequences that do not require all cells to consider changes at every time step in model evolution. The implications of departing from regular grid arrays have also been explored.

Opinions differ as to the usefulness of CA-based models in geography. Although the potential for developing models that intrinsically capture how local interactions scale up to create global patterns is welcome, for some the framework is too restrictive for the development of truly useful simulation models. However, the pedagogic value of simple CA models in showing how local effects can combine to produce unexpected outcomes is widely acknowledged.

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