A Tale of Two Fractals

• Main Author: Kirillov, A.A. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Birkhũser, 2013.
• Subjects: Mathematics.; Algebra.; Global analysis (Mathematics).; Functions, special.; Visualization.; Geometry.; Special Functions.; Analysis.; Applications of Mathematics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-8382-5

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mains...

Table of Contents:

• Introduction
• Part 1. The SierpiDski Gasket
• Definition and General Properties
• The Laplace Operator on the SierpiDski Gasket.- Harmonic Functions on the SierpiDski Gasket
• Part 2. The Apollonian Gasket
• Introduction
• Circles and Disks on Spheres
• Definition of the Apollonian Gasket
• Arithmetic Properties of Apollonian Gaskets
• Geometric and Group-Theoretic Approach
• Many-Dimensional Apollonian Gaskets
• Bibliography.