         Spatial Change Analysis Spatial Distribution Analysis of Change Indices Spatial Dynamics Modelling Property changes in space Spatial Dynamics - Discontinuous case Example of CA : Game of Life Example of CA using Markov Chain Example of CA : SLEUTH, a more complex one Spatial Dynamics - Continuous case Summary Recommended Reading Glossary Bibliography Metadata

 GITTA/CartouCHe news:   # Spatial Dynamics - Discontinuous case Cellular automata were invented in the late 1940s by two mathematicians, John von Neumann and Stanislaw Ulam, working at the Los Alamos National Laboratory in the United States. Cellular Automata (CA) are dynamic systems which are discrete in space and time, operate on a uniform, regular lattice and are characterised by "local" interactions.

A CA system consists of a regular grid of cells; each can be in one of a finite number updated synchronously in discrete time steps:

• The state of a cell is determined by the previous states of the surrounding neighbourhood of cells.
• Each cell in a regular spatial lattice can have any one of a finite number of states.
• Local rule: the state of a cell at a given time depends only on its own state one time step previously and states of its nearby neighbours at the previous time step. The state of the entire lattice advances in discrete time steps

Different kind of problems can be approached using cellular structure and rules: spatially complex systems (e.g., landscape processes), discrete entity modelling in space and time (e.g., ecological systems, population dynamics) or emergent phenomena (e.g., evolution, earthquakes)

CA consist of different elements, they are: The two considered spatial neighbourhoods: limited neighbourhood (Von Neumann) and extended (Moore).

As summarised by A.K. Singh (2003), a cellular automata model can be represented as the following quadruple: Then the state of a cell at time (t+1) is a function of it state at time t of its neighbourhood and of the set of transition rules:     