Hausdorff dimension of the limit sets of some planar geometric constructions
This interesting paper concerns the Hausdorff and box dimensions of the limit sets for various geometric constructions in the plane. In the introduction, the author gives a comprehensive survey of results known for extensions of the class of selfsimilar sets, in particular for Moran constructions and (more general) Moran-like constructions. For a Moran-like construction the Hausdorff dimension and the box dimension of the limit set coincide. He also gives a survey of results known for some special non-Moran-like constructions for which these two fractal dimensions can be computed rigorously. In particular, in 1984, Bedford and McMullen computed independently these dimensions for some self-affine limit sets known as the generalized Sierpiński carpets. The author's new results concern a general class of non-Moran-like planar geometric constructions, called the rectangle-like constructions. This class is essentially larger than that with self-affine limit sets. In particular, he computed the Hausdorff and the box dimension of the flexed Sierpiński gasket defined by Rudnik in 1989.
scientific article; zbMATH DE number 5132554
scientific article