Manhattan property of geodesic paths on self-affine carpets

DOI10.1007/s00013-018-1199-4zbMath1400.28017OpenAlexW2805869028WikidataQ129737381 ScholiaQ129737381MaRDI QIDQ1660098

Yiming Li, Li-Feng Xi

Publication date: 23 August 2018

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-018-1199-4

zbMATH Keywords

fractalself-affine carpetManhattan distancerectificable curve

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Fractals (28A80)

Related Items (11)

Weighted average geodesic distance of Vicsek network ⋮ GEODESICS IN THE SIERPINSKI CARPET AND MENGER SPONGE ⋮ INHERENT FEATURES OF FRACTAL SETS AND KEY ATTRIBUTES OF FRACTAL MODELS ⋮ Unnamed Item ⋮ ARITHMETIC ON MORAN SETS ⋮ VISIBILITY OF CARTESIAN PRODUCTS OF CANTOR SETS ⋮ Differentiable points of Sierpinski-like sponges ⋮ MULTIPLE REPRESENTATIONS OF REAL NUMBERS ON SELF-SIMILAR SETS WITH OVERLAPS ⋮ Mean geodesic distance of the level-\(n\) Sierpinski gasket ⋮ Estimating the Hausdorff dimensions of univoque sets for self-similar sets ⋮ AVERAGE DISTANCE OF SIERPINSKI-LIKE CARPET

Cites Work

• Periodic billiard orbits of self-similar Sierpiński carpets
• Rectifiable curves in Sierpinski carpets
• The Hausdorff dimension of general Sierpiński carpets
• The Hausdorff dimension of self-affine fractals
• Self-affine sets in analytic curves and algebraic surfaces
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