  Deterministic and time-reversible nonequilibrium molecular dynamics
simulations typically generate "fractal" [ fractional-dimensional ] phase-space
distributions. Because these distributions and their time-reversed twins have
zero phase volume, stable attractors "forward in time" and unstable
(unobservable) repellors when reversed, these simulations are consistent with
the Second Law of Thermodynamics. These same reversibility and stability
properties can also be found in compressible Baker Maps, or in their equivalent
random walks, motivating their careful study. We illustrate these ideas with
three examples: a Cantor-Set Map and two linear compressible Baker Maps,
N2$(q,p)$ and N3$(q,p)$. The two Baker Maps' Information dimensions estimated
from sequential mappings agree while those from pointwise iteration do not,
with the estimates dependent upon details of the approach to the maps'
nonequilibrium steady states.
