VecGCA: a vector-based geographic cellular automata model allowing geometric transformations of objects

Cellular automata (CA) can reproduce global patterns and behavior from local interactions of cells and they are used increasingly to simulate complex natural and human systems. Among their attributes are their computational simplicity and their explicit representation of space and time. However, the classic definition of CA limits their application to problems that involve a discrete space, and similar rules and neighborhoods for all cells. In addition, the standard raster-based CA model is sensitive to spatial scale. This paper presents a new vector-based geographic cellular automata model, called the VecGCA model, which defines space as a collection of irregular geographic objects. Each object has a geometric representation (a polygon) that evolves through time according to a transition function that depends on the influence of neighboring polygons. In this model, the neighborhood is defined as the region of influence on each geographic object, and the neighbors are all geographic objects located within the region of influence. An innovative aspect of the VecGCA model is that the procedure allows geometric transformation of objects. The area of a polygon (representing an object) is reduced in the region that is nearest to the neighbor that exerts an influence on it, and the area of that neighbor is increased accordingly. The proposed model was tested with real data and compared with a raster-based CA model to simulate land-use changes in an agroforested area in southern Quebec, Canada. The model was validated using two land-use maps, produced from satellite Landsat Thematic Mapper imagery, which were acquired in 1999 and 2002. The results obtained show that VecGCA can represent well the dynamics in the study area through an adequate evolution of the geometry of the geographic objects which are independent of the cell size, whereas, to generate similar outcomes in the raster-based CA model, a sensitivity analysis must be conducted to determine which cell size is needed. The geometric transformation procedure introduced in the VecGCA model executes the change of shape of a geographic object by changing its state in a portion of its surface, allowing a more realistic representation of the evolution of the landscape.