The study of affine hypersurfaces occupies a central role in differential geometry, providing deep insights into both the intrinsic and extrinsic properties of submanifolds in affine spaces. This ...

Self-affine tiles and fractal geometry form a rich field where geometric precision meets the complexity of nature’s form. At its core, the subject examines how self-affine tiles—constructed via affine ...

This is a preview. Log in through your library . Abstract Necessary and sufficient conditions are given for a lattice L to be the lattice of flats of an affine space of arbitrary (possibly infinite) ...

For a self–similar or self–affine tile in ℝn we study the following questions: (1) What is the boundary? (2) What is the convex hull? We show that the boundary is a graph directed self–affine fractal, ...