Continuous spatial automata, unlike cellular automata, have a continuum of locations. The state of a location is a finite number of real numbers. Time is also continuous, and 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 zebras and spots on leopards. When these are approximated by CA, such CAs often yield similar patterns. MacLennan [1] considers continuous spatial automata as a model of computation. A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... Reaction–diffusion systems are mathematical models that describe how the concentration of one or more substances change under the influence of two processes: chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. ... Alan Mathison Turing, OBE (June 23, 1912 – June 7, 1954), was an English mathematician, logician, and cryptographer. ... Species Equus zebra Equus hartmannae Equus quagga Equus grevyi The Zebra is a part of the horse family, Equidae, native to central and southern Africa. ...

There are known examples of continuous spatial automata which exhibit propagating phenomena analogous to gliders in Conway's Game of Life. For example, take a 2-sphere, and attach a handle between two nearby points on the equator; because this manifold has Euler characteristic zero, we may choose a continuous nonvanishing vector field pointing through the handle, which in turns implies the existence of a Lorentz metric such that the equator is a closed timelike geodesic. An observer free falling along this geodesic falls toward and through the handle; in the observer's frame of reference, the handle propagates toward the observer. This example generalizes to any Lorentzian manifold containing a closed timelike geodesic which passes through relatively flat region before passing through a relatively curved region. Because no closed timelike curve on a Lorentzian manifold is timelike homotopic to a point (where the manifold would not be locally causally well behaved), there is some timelike topological feature which prevents the curve from being deformed to a point. Because it has been conjectured that these might serve as a model of a photon, these are sometimes also called pseudo-photons. Gospers Glider Gun creating gliders. The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. ... For other uses, see sphere (disambiguation). ... It has been suggested that Vertex/Face/Edge relation in a convex polyhedron be merged into this article or section. ... In differential geometry, a pseudo-Riemannian manifold is a smooth manifold equipped with a smooth, symmetric, tensor which is nondegenerate at each point on the manifold. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... A frame of reference is a particular perspective from which the universe is observed. ... In differential geometry, a pseudo-Riemannian manifold is a smooth manifold equipped with a smooth, symmetric, tensor which is nondegenerate at each point on the manifold. ... From the point of view of general relativity, a closed timelike curve (CTC) is a worldline of a material particle in spacetime that is closed. ...

It is an important open question whether pseudo-photons can be created in an Einstein vacuum space-time, in the same way that a glider gun in Conway's Game of Life fires off a series of gliders. If so, it is argued that pseudo-photons can be created and destroyed only in multiples of two, as a result of energy-momentum conservation.