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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.
[[Category:Cellular automata]]
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