A brane world model is investigated, in which there are many branes that ma
y intersect and self-intersect. One of the branes, being a 3-brane, represe
nts our spacetime, while the other branes, if they intersect our brane worl
d, manifest themselves as matter in our 3-brane. It is shown that such a ma
tter encompasses dust of point particles and higher-dimensional p-branes, a
nd all those objects follow "geodesics" in the world volume swept by our 3-
brane. We also point point out that such a model can be formulated in a bac
kground independent way, and that the kinetic term for gravity arises from
quantum fluctuation of the brane. (C) 2001 Elsevier Science B.V. All rights
reserved.