  We study non-terminating graph rewriting models, whose local rules are
applied non-deterministically -- and yet enjoy a strong form of determinism,
namely space-time determinism. Of course in the case of terminating computation
it is well-known that the mess introduced by asynchronous rule applications may
not matter to the end result, as confluence conspires to produce a unique
normal form. In the context of non-terminating computation however, confluence
is a very weak property, and (almost) synchronous rule applications is always
preferred e.g. when it comes to simulating dynamical systems. Here we provide
sufficient conditions so that asynchronous local rule applications conspire to
produce well-determined events in the space-time unfolding of the graph,
regardless of their application orders. Our first example is an asynchronous
simulation of a dynamical system. Our second example features time dilation, in
the spirit of general relativity.
