Self-affine sets with fibered tangents

We study tangent sets of strictly self-affine sets in the plane. If a set in this class satisfies the strong separation condition and projects to a line segment for sufficiently many directions, then for each generic point there exists a rotation $\mathcal{O}$ such that all tangent sets at that point are either of the form $\mathcal{O}((\mathbb{R}\times C)\cap B(0,1))$, where $C$ is a closed porous set, or of the form $\mathcal O((\ell \times { 0 }) \cap B(0,1))$,where$\ell$ is an interval.