  We consider a two-point spatial lattice approximation to an open string
moving in a flat background with B field. It gives a constrained dipole system
under the influence of a vector potential. Solving and quantizing this system
recover all the essential features of a noncommutative space. In particular,
open string interactions induce a canonical product structure on the Hilbert
space of the dipole system. It coincides with the usual star product, even
though the position operators can be thought of as mutually commuting.
Modification of gauge transformations in this noncommutative space also
naturally emerges.
