  There are physically realistic classical systems which exhibit both of these features, of which the best known is perhaps Lorenz’s model of atmospheric convection (Smith 1998: §1.4; Earman 1986: 165). The combination of these two features permits very interesting behaviour—while the existence of an attractor means that over time the states of the system will converge to the region of the attractor, the sensitive dependence on initial conditions means that close states, at any time, will end up arbitrarily far apart. For this to happen the attractor must have a very complex shape (it will be a region of small measure, but most of the state space will be in the neighbourhood of the attractor). More importantly for our purposes, a system with these characteristics, supposing that the divergence under evolution of close states happens quickly enough, will yield behaviour close to Bernoulli—it will yield rapid mixing (Luzzatto et al.  2005).[20]  Roughly, a system is mixing iff the presence of the system in coarse state at one time is probabilistically independent of its presence in another coarse state at another time, provided there is a sufficient amount of time between the two times. This is weaker than Bernoulli (since the states of a Bernoulli system are probabilistically independent if there is any time between them), but still strong enough to plausibly yield a random sequence of outcomes from a coarse grained partition of the state space, sampled infrequently enough. So we do seem to have physically realistic systems that yield random behaviour without chance. (See also the systems discussed in Frigg 2004.)