  This paper proposes a dynamical notion of discrete geodesics, understood as
straightest trajectories in discretized curved spacetime. The notion is
generic, as it is formulated in terms of a general deviation function, but
readily specializes to metric spaces such as discretized pseudo-riemannian
manifolds. It is effective: an algorithm for computing these geodesics
naturally follows, which allows numerical validation---as shown by computing
the perihelion shift of a Mercury-like planet. It is consistent, in the
continuum limit, with the standard notion of timelike geodesics in a
pseudo-riemannian manifold. Whether the algorithm fits within the framework of
cellular automata is discussed at length. KEYWORDS: Discrete connection,
parallel transport, general relativity, Regge calculus.
