  The shell map is a very simple representation of the structure of foams,
combining the geometrical (random tiling) and dynamical (loss of information
from an arbitrary cell out) aspects of disorder. The structure is built from
the central cell outward like an ever expanding jigsaw puzzle without boundary.
The radial map, from one spherical layer of cells to the next, is the logistic
map, and the geometrical tiling is expressed mathematically as a dynamical
system. The isotropy of the disordered structure is expressed locally by
averaging over each layer. The over-all translational invariance is manifest in
the independence of the structure and properties on the choice of the central
cell. The radial map from one layer to the next includes both effects of
disorder and of space curvature. We will illustrate it and give several
examples, including a few arising from discussions in Cargese.
