'''Continuous spatial automata''', unlike [[cellular automata]], have a continuum of locations, while the state of a ___location still is any of a finite number of real numbers. Time can also be continuous, and in this case the state evolves according to differential equations.
One important example is [[reaction-diffusion]] textures, differential equations proposed by [[Alan Turing]] to explain how chemical reactions could create the stripes on [[zebra]]s and spots on leopards. When these are approximated by CA, such CAs often yield similar patterns. Another important example is neural fields, continuum limit [[neural networks]] where average firing rates evolve based on [[Integro-differential_equation|integro-differential equationsequation]]s.<ref>H R Wilson and J D Cowan. Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12:1–24, 1972.</ref><ref>H R Wilson and J D Cowan. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13:55–80, 1973.</ref>. Such models demonstrate spatiotemporal [[pattern formation]], localized states and travelling waves.<ref>S Amari. Dynamics of pattern formation in lateral inhibition type neural fields. Biological Cybernetics, 27:77–87, 1977.</ref><ref>http://www.scholarpedia.org/article/Neural_fields</ref> They have been used as models for cortical memory states and visual hallucinations.<ref>G B Ermentrout and J D Cowan. A mathematical theory of visual hallucination patterns. Biological Cybernetics, 34:137–150, 1979.</ref>
MacLennan [http://www.cs.utk.edu/~mclennan/contin-comp.html] considers continuous spatial automata as a model of computation, and demonstrated that they can implement Turing-universality.<ref>David H. Wolpert and Bruce J. MacLennan, A Universal Field Computer That is Purely Linear, University of Tennessee, Knoxville, Department of Computer Science Technical Report CS-93-206, September 14, 1993, 28 pp. http://web.eecs.utk.edu/~mclennan/papers/ut-cs-93-206.pdf</ref>.
