We investigate the Hall conductivity in a Sierpinski carpet, a fractal of Hausdorff dimension $d_f=ln(8)/ln(3) approx 1.893$, subject to a perpendicular magnetic field. We compute the Hall conductivity using linear response and the recursive Green fu
nction method. Our main finding is that edge modes, corresponding to a maximum Hall conductivity of at least $sigma_{xy}=pm frac{e^2}{h}$, seems to be generically present for arbitrary finite field strength, no mater how one approaches the thermodynamic limit of the fractal. We discuss a simple counting rule to determine the maximal number of edge modes in terms of paths through the system with a fixed width. This quantized edge conductance, as in the case of the conventional Hofstadter problem, is stable with respect to disorder and thus a robust feature of the system.
