  The notion of sprays introduced by Lapidus and his co-workers has proved
useful in the context of fractal tube formulas. In the present note, we propose
a more general concept of sprays, where we allow several generators to make
them more convenient for applications to graph-directed fractals. Using a
simple functional equation satisfied by the volume of the inner
$\varepsilon$-neighborhood of such a generalized spray, we establish a tube
formula for them.
