  Center projection of SU(2) lattice gauge theory allows to isolate magnetic
vortices as confining configurations. The vortex density scales according to
the renormalization group, implying that the vortices are physical objects
rather than lattice artifacts. Here, the binary correlations between points at
which vortices pierce a given plane are investigated. We find an attractive
interaction between the vortices. The correlations show the correct scaling
behavior and are therefore physical. The range of the interaction is found to
be (0.4 +/- 0.2) fm, which should be compared with the average planar vortex
density of approximately 2 vortices/fm^2. We comment on the implications of
these results for recent discussions of the Casimir scaling behavior of higher
dimensional representation Wilson loops in the vortex confinement picture.
