  This paper introduces complexes of linear varieties, called inclics (for
INductively Constructible LInear ComplexeS). As examples, we study galaxies
(these are constructed starting with a star configuration to which we add
general points in a larger projective space). By assigning an order of
vanishing (i.e., a multiplicity) to each member of the complex, we obtain fat
linear varieties (fat points if all of the linear varieties are points). The
scheme theoretic union of these fat linear varieties gives an inclic scheme
$X$. For such a scheme, we show there is an inductive procedure for computing
the Hilbert function of its defining ideal $I_X$, regardless of the choice of
multiplicities. As an application, we show how our results allow the
computation of the Hilbert functions of, for example, symbolic powers
$(I_X)^{(m)}$ for arbitrary $m$ of many new examples of radical ideals $(I_X)$,
and we explicitly compute the Waldschmidt constants $\gamma(I_X)$ for galactic
inclics $X$.
