  The cascading gravity model was proposed to eliminate instabilities of the
original DGP model by embedding our 4D universe into a 5D brane, which is
itself embedded in a 6D bulk. Thus gravity cascades from 6D down to 4D as we
decrease the length scales. We show that it is possible to extend this setup to
lower dimensions as well, i.e. there is a self-consistent embedding of a 3D
brane into a 4D brane, which is itself embedded in a 5D bulk and so on. This
extension fits well into the "vanishing dimensions" framework in which
dimensions open up as we increase the length scales.
