  We discuss recently discovered links of the statistical models of normal
random matrices to some important physical problems of pattern formation and to
the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix
model with a general statistical weight describes dynamics of the interface
between two incompressible fluids with different viscousities in a thin plane
cell (the Saffman-Taylor problem). The latter appears to be mathematically
equivalent to the growth of semiclassical 2D electronic droplets in a strong
uniform magnetic field with localized magnetic impurities (fluxes), as the
number of electrons increases. The equivalence is most easily seen by relating
the both problems to the matrix model.
