An example of fractal singular homogenization

We construct a sequence of quadratic weighted energy forms in an open domain of the plane, which M-converges to the an energy form with a singular fractal term. The weights belong to the A_2-Muckenoupt class and have point-wise singularities. The result implies the spectral convergence of a sequence of second-order weighted elliptic operators in divergence form in the plane to a singular elliptic operator with a second order fractal term.