  We study the space ${\mathcal X}^{d}(G)$ of pictures of a graph $G$ in
complex projective $d$-space. The main result is that the homology groups (with
integer coefficients) of ${\mathcal X}^{d}(G)$ are completely determined by the
Tutte polynomial of $G$. One application is a criterion in terms of the Tutte
polynomial for independence in the {\it $d$-parallel matroids} studied in
combinatorial rigidity theory. For certain special graphs called
\defterm{orchards}, the picture space is smooth and has the structure of an
iterated projective bundle. We give a Borel presentation of the cohomology ring
of the picture space of an orchard, and use this presentation to develop an
analogue of the classical Schubert calculus.
