  We construct classes of two-dimensional aperiodic Lorentz systems that have
infinite horizon and are 'chaotic', in the sense that they are (Poincar\'e)
recurrent, uniformly hyperbolic, ergodic, and the first-return map to any
scatterer is $K$-mixing. In the case of the Lorentz tubes (i.e., Lorentz gases
in a strip), we define general measured families of systems (\emph{ensembles})
for which the above properties occur with probability 1. In the case of the
Lorentz gases in the plane, we define families, endowed with a natural metric,
within which the set of all chaotic dynamical systems is uncountable and dense.
