Fractal Geometry: Mathematical Foundations and Applications

Author: Kenneth Falconer
Publisher:
Publish Date: 2001-07-01
Features: The concept of fractal geometry was first proposed by B. Mandelbrot in 1975. Over the past decade, it has rapidly developed into a new branch of mathematics. It is a powerful theoretical tool for studying and handling irregular shapes in nature and engineering, with applications spanning nearly all fields of natural science, even social sciences, and practically serving to connect various disciplines of modern science. It is often referred to alongside dissipative structures and chaos theory as one of the three major scientific discoveries of the mid-1970s. This book is a new monograph on the theory and applications of fractal geometry, first published in the UK in 1990. The first part explains the basic theory of fractal geometry, primarily focusing on the definition and computational techniques of fractal dimensions. The second part extensively introduces the applications of fractal theory in various aspects of mathematics and physics. This book integrates the theory and applications of fractal geometry, employing a simple and clear approach with strong readability. The translated version retains the original book's approximately 100 exquisite fractal images, making it an excellent graduate-level textbook suitable for university students, teachers, and scientific and technical personnel interested in fractal theory and its applications.