We present a general molecular framework assembly algorithm that takes a largely arbitrary molecular fragment database and a user-supplied target template graph as input. Automatic assembly of molecular fragments from the database, following a prescribed, user-supplied set of connection rules, then turns the template graph into an actual, chemically reasonable molecular framework. Assembly capabilities of our algorithm are tested by producing several abstract, closed-loop shapes. To indicate a few of many possible application areas we demonstrate a host-guest complex and a road toward catalysis. Postassembly substituent exchange can be used to produce electric fields of desired values at desired points inside the framework or at its surface as a stepping stone toward rationally designed, artificial heterogeneous catalysts.