# 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
- 2018

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)

- MathematicsTURKISH JOURNAL OF MATHEMATICS
- 2019

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

- Mathematics
- 2016

The computation of the distance between any two points of the Sierpinski Gasket with respect to the intrinsic metric has already been investigated by several authors. In the literature there is not…

### GEODESICS IN THE SIERPINSKI CARPET AND MENGER SPONGE

- Mathematics
- 2020

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...

### ECCENTRIC DISTANCE SUM OF SIERPIŃSKI GASKET AND SIERPIŃSKI NETWORK

- MathematicsFractals
- 2019

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…

### DISTRIBUTION OF DISTANCES AND INTERIOR DISTANCES FOR CERTAIN SELF-SIMILAR MEASURES

- Mathematics
- 2004

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

- MathematicsArs Comb.
- 2014

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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