  Geometrically, foams or covalent graphs can be decomposed into successive
layers or strata. Disorder of the underlying structure imposes a characteristic
roughening of the layers. Our main results are hysteresis and convergence in
the layer sequences. 1) If the direction of construction is reversed, the
layers are different in the up and down sequences (irreversibility);
nevertheless, under suitable but non-restrictive conditions, the layers come
back, exactly, to the initial profile, a hysteresis phenomenon. 2) Layer
sequences based on different initial conditions (e.g. different starting cells)
converge, at least in the cylindrical geometry. Jogs in layers may be
represented as pairs of opposite dislocations, moving erratically due to the
disorder of the underlying structure and ending up annihilating when colliding.
