m:n-CA(k)

Wed, 2009-05-20 14:12 | pau

A multi-n-dimensional cellular automata m:n-CA^k is a generalization of a cellular automata defined as follows:

Its representation is:

m:n-CA^k

Where

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-AC^k over Z2 is shown.
	In this video a simple evolution rule for a m:n-AC^k over R2 is shown. Here we are not using any simplification rule to reduce the number of points added to the surface.