Dimension of slices of Sierpiński-like carpets
Balázs Bárány
Polish Academy of Sciences, Warsaw, PolandMichał Rams
Polish Academy of Sciences, Warsaw, Poland
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Abstract
We investigate the dimension of intersections of the Sierpiński-like carpets with lines. We show a sufficient condition that for a fixed rational slope the dimension of almost every intersection with respect to the natural measure is strictly greater than , and almost every intersection with respect to the Lebesgue measure is strictly less than , where s is the Hausdorff dimension of the carpet. Moreover, we give partial multifractal spectra for the Hausdorff and packing dimension of slices.
Cite this article
Balázs Bárány, Michał Rams, Dimension of slices of Sierpiński-like carpets. J. Fractal Geom. 1 (2014), no. 3, pp. 273–294
DOI 10.4171/JFG/8