  We report the presence of multiple flat bands in a class of two-dimensional
(2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic
unit cells. Solving the tight-binding Hamiltonian for such lattices with
different generations of a SPG network, we find multiple degenerate and
non-degenerate completely flat bands, depending on the configuration of
parameters of the Hamiltonian. Moreover, we find a generic formula to determine
the number of such bands as a function of the generation index $\ell$ of the
fractal geometry. We show that the flat bands and their neighboring dispersive
bands have remarkable features, the most interesting one being the spin-1
conical-type spectrum at the band center without any staggered magnetic flux,
in contrast to the Kagome lattice. We furthermore investigate the effect of the
magnetic flux in these lattice settings and show that different combinations of
fluxes through such fractal unit cells lead to richer spectrum with a single
isolated flat band or gapless electron- or hole-like flat bands. Finally, we
discuss a possible experimental setup to engineer such fractal flat band
network using single-mode laser-induced photonic waveguides.
