I don't think there's much agreement about the exact, formal definition of fractal, but "Hausdorff dimension greater than the topological dimension" is probably

I don't think there's much agreement about the exact, formal definition of fractal, but "Hausdorff dimension greater than the topological dimension" is probably a better one than "Hausdorff dimension is not an integer". Otherwise, not even the boundary of the Mandelbrot set is a fractal! (It has Hausdorff dimension 2).