Fractal hierarchy dissipative structures (FHDS) can quite possibly manifest new non-phonon type of magnetic ordering. In this paper we formulate the principles of FHDS formation from microscopic to macroscopic levels, determine physico-chemical criteria for picking up a suitable heteroaromatic system as well as the type of metal to obtain fractal ferromagnetism. Conditions of fractal ferromagnetism existance can be deduced from the Stoner’s criterion of ferromagnetism in Hubbard model applied to fractal geometry.