MPhil in Mathematics - Average Geodesic Distance on Sierpiński Triangles
2:00pm - 5:00pm
Room 2612A (near lifts 31&32)
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 Sierpi_nski triangle T was 466=885. They used the relation
between paths on T and the game graph of the Tower of Hanoi and Sierpinski 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. We will also verify that we can arrive the same value as Hinz and Schief obtained as well.
Hinz and Schief (1990) have proved that the average geodesic distance between any two points on the Sierpi_nski triangle T was 466=885. They used the relation
between paths on T and the game graph of the Tower of Hanoi and Sierpinski 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. We will also verify that we can arrive the same value as Hinz and Schief obtained as well.