  We first establish any continuum without interiors can be a limit set of
iterations of an entire function on an oscillating wandering domain, and hence
arise as a component of Julia sets. Recently, Luka Boc Thaler showed that every
bounded connected regular open set, whose closure has a connected complement,
is an oscillating or an escaping wandering domain of some entire function. A
natural question is: What kind of domains can be realized as a periodic domain
of some entire function? In this paper, we construct a sequence of entire
functions whose invariant Fatou components can be approached to a regular
domain.
