  We investigate 4-quark ($qq\bar{q}\bar{q}$) systems as well as multi-quark
states with a large number of quarks and anti-quarks using the chromodielectric
model. In the former type of systems the flux distribution and the
corresponding energy of such systems for planar and non-planar geometries are
studied. From the comparison to the case of two independent $q\bar{q}$-strings
we deduce the interaction potential between two strings. We find an attraction
between strings and a characteristic string flip if there are two degenerate
string combinations between the four particles. The interaction shows no strong
Van-der-Waals forces and the long range behavior of the potential is well
described by a Yukawa potential, which might be confirmed in future lattice
calculations. The multi-quark states develop an inhomogeneous porous structure
even for particle densities large compared to nuclear matter constituent quark
densities. We present first results of the dependence of the system on the
particle density pointing towards a percolation type of transition from a
hadronic matter phase to a quark matter phase. The critical energy density is
found at $\epsilon_c = 1.2 GeV/fm^3$.
