A layered uniaxial dielectric structure is considered. The layers in the structure are distributed according to a one-dimensional fractal set. The resulting fractal metamaterial is homogenized with an original source-driven homogenization approach which is suitable for both numerical and analytical calculations. Due to the fact that the considered metamaterial is nonmagnetic, the only effective parameter which needs to be calculated is the effective permittivity dyadic e(ω, k). The effective permittivity is obtained analytically (by using a transfer matrix approach) and numerically (by using a Finite-Difference Time-Domain solver).