Imaginary Hypercubes

Tsuiki, Hideki; Tsukamoto, Yasuyuki

doi:10.1007/978-3-319-13287-7_15

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2016

2022

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Cited by 3 publications

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“…As particular examples of such fractal three-dimensional objects, fractal imaginary cubes are defined and investigated in [15,17]. An imaginary cube is an object which has square projections in three orthogonal directions just as a cube has.…”

Section: Introductionmentioning

confidence: 99%

Projected images of the Sierpinski tetrahedron and other fractal imaginary cubes

Tsuiki¹

2022

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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 p OP + q OQ + r OR = 0 for odd numbers p, q, r. This fact was essentially obtained by Kenyon in [7]. We reformulate his proof through the notion of projection of differenced digit set so that it could be applied to projections of other fractal objects. We study projections of H fractal and T fractal as well as Sierpinski tetrahedron, which are the fractal imaginary cubes of the first two levels. We characterize the directions from which these fractals are projected to sets with positive measures.

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Section: Introductionmentioning

confidence: 99%