  A systematic analytic treatment of fluctuations in Laplacian growth is given.
The growth process is regularized by a short-distance cutoff $\hbar$ preventing
the cusps production in a finite time. This regularization mechanism generates
tiny inevitable fluctuations on a microscale, so that the interface dynamics
becomes chaotic. The time evolution of fluctuations can be described by the
universal Dyson Brownian motion, which reduces to the complex viscous Burgers
equation in the hydrodynamic approximation. Because of the intrinsic
instability of the interface dynamics, tiny fluctuations of the interface on a
microscale generate universal patterns with well developed fjords and fingers
in a long time asymptotic.
