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- W4281692020 abstract "A projected image of a Sierpinski tetrahedron has a positive measure if and only if the images O, P, Q, R of the four vertices satisfy pOP + qOQ + rOR = 0 for odd integers p, q, r. This fact was essentially obtained by Kenyon (Symbolic dynamics and its applications 135, 1992). We reformulate his proof through the notion of projection of differenced radix expansion sets and obtain similar results for other fractal objects. Specifically, we study projections of H-fractal and T-fractal as well as Sierpinski tetrahedron, which are fractal imaginary cubes (i.e., fractal objects that are projected to squares along three orthogonal directions just as a cube) of the first two degrees, and characterize the directions from which these fractals are projected to sets with positive measures." @default.
- W4281692020 created "2022-06-13" @default.
- W4281692020 creator A5027497864 @default.
- W4281692020 date "2022-05-25" @default.
- W4281692020 modified "2023-09-23" @default.
- W4281692020 title "Projected images of the Sierpinski tetrahedron and other fractal imaginary cubes" @default.
- W4281692020 doi "https://doi.org/10.48550/arxiv.2205.13065" @default.
- W4281692020 hasPublicationYear "2022" @default.
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