tech report: continuous spatial automata

[mclennan@cs.utk.edu]

The following technical report is now available:

                   Continuous Spatial Automata

                         B. J. MacLennan

                 Department of Computer Science
                     University of Tennessee
                    Knoxville, TN 37996-1301
                      maclennan at cs.utk.edu

                            CS-90-121
                        November 26, 1990

                            ABSTRACT

A _continuous_spatial_automaton_ is analogous to a cellular auto-
maton, except that the cells form a continuum, as do the possible
states of the cells.  After an informal mathematical description
of spatial automata, we describe in detail a continuous analog of
Conway's ``Life,'' and show how the automaton can be implemented
using the basic operations of field computation.

     Typically a cellular automaton has a finite (sometimes denu-
merably infinite) set of cells, often arranged in a one or two
dimensional array. Each cell can be in one of a number of states.
In contrast, a continuous spatial automaton has a one, two or
higher dimensional continuum of _loci_ (corresponding to cells),
each of which has a state drawn from a continuum (typically [0,1]).
The state is required to vary continuously with the locus.
In a cellular automaton there is a transition function that
determines the state of a cell at the next time step based on the
state of it and a finite number of neighbors at the current time
step.  A discrete-time spatial automaton is very similar:  the
future state of a locus is a continuous function of the states of
the loci in a (closed or open) bounded neighborhood of the given
locus.

The report is available as a compressed postscript file in the
pub/neuroprose subdirectory; it may be obtained with the Getps
script:

     Getps maclennan.csa.ps.Z

For HARDCOPY send your address to:  library at cs.utk.edu

For other correspondence:

Bruce MacLennan
Department of Computer Science
107 Ayres Hall
The University of Tennessee
Knoxville, TN 37996-1301

(615)974-0994/5067
maclennan at cs.utk.edu