Many models use discrete time steps, such as 10 minutes, one month, or a year for each time step. Usually during one model time period all rules are applied to each cell in order for all rows and columns of cells in the framework, with the new states going into a replica buffer grid, then the replica replaces the original. For example in Conway’s game of Life described above, setting all cells to dead will produce no change, while setting all cells to alive will make all cells die in just one iteration, a phase change. The choice of initial conditions is important. The initial conditions are the start set or seed generation for the model, usually an actual spatial configuration or map of the phenomenon at the start period for the modeling, such as a land use map of a city in 2010, when the goal is to simulate changes to 2030. White cells are “dead”, and black “alive.” The initial conditions and further time steps for the Game of Life. In the design of geographical CA models, the rules set and its construction, or derivation from actual change data, is often a major part of the CA model design task.įigure 1. Figure 1 shows an initial distribution of live cells, and the configuration after sequences of time steps. At each step in time, two rules are applied based on how many of the neighbors are alive: a live cell will die if it has fewer that two or more than three live neighbors a dead cell will come to life if it has exactly three live neighbors otherwise it remains unchanged (Gardner, 1970 1972). Simple CA models have few rules, for example in Conway’s classic 1970 CA game of Life (Adamatzky, 2010), cells can only have the states alive (1) or dead (0) on a square grid with an 8 cell neighborhood. The rules are the determinants of the conditions under which the active cell will change states. All cells in the CA must be in one of these states at every time period. For example, the set of states for a land use cell could be. Cells are also defined as having mutually exclusive states, a set of classes to which the cell can belong. Changes within a cell are made by applying the rules within the neighborhood, and changing the cell if the situation warrants it. In classical CA, this is the immediately adjacent two cells in one dimension and the Moore (8) or Von Neumann (4) neighbors in two dimensions. The neighborhood is the region of interaction among the cells. Geographical data for CA are often chosen to coincide with satellite image pixels or geographic grids, that are already partitioned into tessellations. Cells are identical spatial units, often squares or pixels, that cover the geographic extent at a chosen resolution. Geographical examples usually choose a study area or region, and mask the extent so that the CA cannot apply beyond them. The framework sets the constraints and limits of the system, for example constraining a CA to one or two dimensions, and deciding what happens at a region’s edges. Advantages of CA models are that they are simple, nominally deterministic yet capable of showing phase changes and emergence, map easily onto the data structures used in geographic information systems, and are easy to implement and understand.Ī CA consists of six defining components: a framework, cells, a neighborhood, rules, initial conditions and an update sequence. CA are among the simplest ways in which complex systems behavior can be demonstrated, and consequently have been popular in modeling geographic systems that show complexity, including land use change, urban growth, human and vehicle movement, the spread of disease, sand dune formation, and vegetation change. The states of all cells in the framework are updated simultaneously in discrete time steps during which the state of each cell is changed according to a set of rules that depend on the state of the cell and those of its neighbors at the previous time step.Ĭellular automata (CA) are computational abstractions that allow simulations of spatially distributed phenomena and their dynamics over time. Cellular automata: A regular framework of cells, each in one of a finite number of states.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |