  Invoking an initial symmetry between the time $ t $ and some extra spatial
dimension $ y $, we discuss a novel scenario where the dynamical formation of
the 4-dim brane and its cosmological evolution are induced simultaneously by a
common $ t<->y $ symmetry breaking mechanism. The local maximum of the
underlying scalar potential is mapped onto a 'watershed' curve in the $ (t,y) $
plane; the direction tangent to this curve is identified as the cosmic time,
whereas the perpendicular direction serves locally as the extra spatial
dimension. Special attention is devoted to the so-called slinky configurations,
whose brane cosmology is characterized by a decaying cosmological constant
along the watershed curve. Such a slinky solution is first constructed within a
simplified case where the watershed is constrained by $ y = 0 $. The physical
requirements for a slinky configuration to generate a realistic model of
cosmological evolution are then discussed in a more elaborated framework.
