The solvable model of a periodic array of quantum dots in a magnetic f
ield is investigated. It is shown that in the case of square lattice a
nd irrational flux the energy spectrum of a charged particle in the ar
ray has a fractal structure. In the case of honeycomb lattice the exis
tence of an additional splitting of magnetic bands related with lattic
e geometry. The position of the Van Hove singularities is determined.