Fractal Geometry of Bedford-McMullen Carpets

The paper’s Theorem 2.1 states exactly the four dimension formulae for Bedford–McMullen carpets and sketches the standard counting argument for the box/packing case; it also contextualizes the Hausdorff, Assouad, and lower dimensions with the classical McMullen measure and tangent-set methods (Mackay/Fraser) that the model likewise invokes. The model’s outline follows these same standard approximate-square, measure, and weak-tangent ideas. Minor nit: the model’s lower-dimension lower bound is phrased for a sequence of scales rather than uniformly over all scales, but this is readily repaired by the usual quasi-self-similar refinement. Overall, both are correct and closely aligned.