Polarizability of 2D monster and light scattering

The electrostatics of 2D system with complicated inner boundary is studied. The object which we call "monster" is built by an iterative process of multiple conformal mapping of the circle exterior. The procedure leads to the figures built from circle with branching curved cuts (i), to the multiple tangential near-round circles (ii) and the Mandelbrot map (iii). The polarizability of a monster in the homogeneous external field is found. The light scattering cross-section was expressed through the polarizability of a monster.