A multi-n-dimensional cellular automata m:n-CAk is a generalization of a cellular automata defined as follows:
Its representation is:
- m is the number of layers in the automata.
- n is the number of dimensions of the layers.
- k is the number of main layers (1 by default).
With this notation, a two-dimensional cellular automata is represented as 1:2-CA. A transition to an m:2-CA cellular automata is defined like a two-dimensional cellular automata, but the main-layer cell state is a combination of the data contained in the same position of the m-1 secondary layers.
GIS data can be represented in different layers of the m:n-CA. Vector data (2DLayers) and raster data (3DLayers) are suitable. All layers must be georeferenced.
An m:n-CA implements a set of rules that determine its transitions. Some new features are included:
- Layers that modify their cell state are called main layers. The maximum number of main layers is m. The number of main layers is represented by k (m>=k). A given automata may have more than one main layer.
- The combination function Ψ allows state calculation in a main layer, which depends on the state in all other layers of the automata.
- Data need not be in raster format since all layers are georeferenced. Thus, vector data may be used in cellular automata. The Ψ function determines the cell state independently of the structure of the layer data.
Obviously, a 1:n-CA (a cellular automata with just one raster layer) is the same as an n-dimensional cellular automata.
Some media related with the project.
|In this video a simple evolution rule for a m:n-ACk over Z2 is shown.|
|In this video a simple evolution rule for a m:n-ACk over R2 is shown. Here we are not using any simplification rule to reduce the number of points added to the surface.|
The computer program (implemented in C++) that are represented in these videos can be downloaded here (windows installer).
If you have a question about the publications please feel free to ask me anything.
5-7th April 2006. University of East Anglia (Norwich) (U.K.)
Marseille, France, October 20-22 2005
5-7th April 2006. Nottingham (U.K.)