Manhattan property of geodesic paths on self-affine carpets
type: Item
instance of: scholarly article
title: Manhattan property of geodesic paths on self-affine carpets
zbMATH Open document ID: 1400.28017
author: Yiming Li
author: Lifeng Xi
published in: Archiv der Mathematik
publication date: 2018-08-23T00:00:00Z
review text: The authors show that, unlike in the case of Bedford-McMullen self-affine carpets, the geodesic path on a self-similar carpet between point \((x_1,y_1)\) and \((x_2,y_2)\) does not have length \(L \geq |x_1-x_2|+|y_1-y_2|\).
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A75
zbMATH DE Number: 6924003
zbMATH Keywords: fractal
zbMATH Keywords: self-affine carpet
zbMATH Keywords: rectificable curve
zbMATH Keywords: Manhattan distance
reviewed by: Peter Massopust
MaRDI profile type: Publication
full work available at URL: s00013-018-1199-4
OpenAlex ID: W2805869028
cites work: Distribution of distances and interior distances for certain self-similar measures
cites work: Periodic billiard orbits of self-similar Sierpiński carpets
cites work: Rectifiable curves in Sierpiński carpets
cites work: Q3241504
cites work: Self-affine sets in analytic curves and algebraic surfaces
cites work: The Hausdorff dimension of general Sierpiński carpets
cites work: The Hausdorff dimension of self-affine fractals
cites work: Fractal geometry. Mathematical foundations and applications
cites work: Q3598569
Wikidata QID: Q129737381
DOI: 10.1007/S00013-018-1199-4
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description: scientific article; zbMATH DE number 6924003