  The continuous packing of a flexible rod in two-dimensional cavities yields a
countable set of interacting domains that resembles non-equilibrium cellular
systems and belongs to a new class of light-weight material. However, the link
between the length of the rod and the number of domains requires investigation
especially in the case of non-simply connected cavities, where the number of
avoided regions emulates an effective topological temperature. In the present
article we report the results of an experiment of injection of a single
flexible rod into annular cavities in order to find the total length needed to
insert a given number of loops (domains of one vertex). Using an exponential
model to describe the experimental data we quite minutely analyze the initial
conditions, the intermediary behavior, and the tight-packing limit. This method
allows the observation of a new fluctuation phenomenon associated with
instabilities in the dynamic evolution of the packing process. Furthermore, the
fractal dimension of the global pattern enters the discussion under a novel
point of view. A comparison with the classical problems of the random close
packing of disks, and jammed disk packings is made.
