Average geodesic distance on Sierpiński triangles

Abstract

Many researchers have investigated the average distance between points on self-similar sets. For example, the Cantor set is studied by Leary et al. (2010) Hinz and Schief (1990) have proved that the average geodesic distance between any two points on the Sierpiński triangle T was 466/885. They used the relation between paths on T and the game graph of the Tower of Hanoi and Sierpiński graphs. In this thesis, we will develop an algorithm to compute the average geodesic distance on T directly and generalize this method to any triangles with integral sides. Also, we will verify that we can arrive the same value as Hinz and Schief obtained as well.

Date of Award	2017
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology