Slicing the Sierpiński gasket
arXiv:1301.7077 · doi:10.1088/0951-7715/25/6/1753
Abstract
We investigate the dimension of intersections of the Sierpiński gasket with lines. Our first main result describes a countable, dense set of angles that are exceptional for Marstrand's theorem. We then provide a multifractal analysis for the set of points in the projection for which the associated slice has a prescribed dimension.
19 pages, 4 figures