  We report a clear evidence of atomic fractals in the nonlinear motion of a
two-level atom in a standing-wave microcavity. Fractal-like structures, typical
for chaotic scattering, are numerically found in the dependencies of outgoing
positions and momenta of scattered atoms on their ingoing values and in the
dependence of exit times of cold atoms on their initial momenta in the generic
semiclassical models of cavity QED (1) with atoms in a far-detuned amplitude
(phase)-modulated standing wave and (2) with coupled atomic external and
internal degrees of freedom. Tiny interplay between all the degrees of freedom
in the second model is responsible for trapping atoms even in a very short
microcavity. It may lead simultaneously, at least, to two kinds of atomic
fractals, a countable fractal (a set of initial momenta generating
separatrix-like atomic trajectories) and a seemingly uncountable fractal with a
set of momenta generating infinite walkings of atoms inside the cavity.
