  One way to describe the entropy of black holes comes from partitioning
momentum charge across fractionated intersecting brane systems. Here we
construct $\frac{1}{8}$-BPS solutions by adding momentum to a maze of M2-brane
strips stretched between M5 branes. Before the addition of momentum, the
$\frac{1}{4}$-BPS supergravity solution describing the maze is governed by a
master function obeying a complicated Monge-Amp\`ere equation. Given such a
solution, we show that one can add momentum waves without modifying the
$\frac{1}{4}$-BPS M2-M5 background. Remarkably, these excitations are fully
determined by a layered set of $\textit{linear}$ equations. The fields
responsible for carrying the momentum are parameterized by arbitrary functions
of a null direction, and have exactly the same structure as in brane
world-volume constructions. The fact that the momentum and flux excitations of
the M2-M5-P system are governed by a linear structure brings us one step closer
to using supergravity solutions to capture the entropy of supersymmetric
black-holes.
