The average distance on the Sierpiński gasket
@article{Hinz1990TheAD, title={The average distance on the Sierpiński gasket}, author={Andreas M. Hinz and Andreas Schief}, journal={Probability Theory and Related Fields}, year={1990}, volume={87}, pages={129-138} }
SummaryThe canonical distance of points on the Sierpiński gasket is considered and its expectation deduced. The solution is surprising, both for the value and for the method derived from an analysis of graphs connected with the Tower of Hanoi problem.
68 Citations
GEODESICS OF THE SIERPINSKI GASKET
- MathematicsFractals
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In this paper, we examine the number of geodesics between two points of the Sierpinski Gasket ([Formula: see text]) via code representations of the points and as a main result we show that the…
The intrinsic metric and geodesics on the Sierpinski gasketSG(3)
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We give an explicit expression for the intrinsic metric on the Sierpinski gasket SG(3) (the mod-3 Sierpinski gasket) via code representation of its points. We also investigate the geodesics of SG(3)…
An Explicit Formula of the Intrinsic Metric on the Sierpinski Gasket via Code Representation
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In this paper, we study geodesics in the Sierpinski carpet and Menger sponge, as well as in a family of fractals that naturally generalize the carpet and sponge to higher dimensions. In all dimensi...
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The eccentric distance sum is concerned with complex networks. To obtain the asymptotic formula of eccentric distance sum on growing Sierpiński networks, we study some nonlinear integral in terms of…
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We determine the distribution of Euclidean and interior distances in the Sierpinski gasket and the detailed structure of shortest paths in the Sierpinski carpet.
A 2-parametric generalization of Sierpinski gasket graphs
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Graphs S[n, k] are introduced as the graphs obtained from the Sierpinski graphs S(n, k) by contracting edges that lie in no complete subgraph Kk. The family S[n, k] is a generalization of a…
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