Average geodesic distance on Sierpiński triangles
by Yau Cheuk Wai
THESIS
2017
M.Phil. Mathematics
viii, 45 pages : illustrations ; 30 cm
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.
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