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 is actually playing a role in connecting various areas 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, mainly focusing on the definition and computational techniques of fractal dimensions. The second part extensively introduces the various applications of fractal theory in mathematics and physics. This book integrates the theory and applications of fractal geometry, employing a simple and clear approach with strong readability. The translation retains the original book's approximately 100 exquisite fractal images, making it an excellent graduate-level textbook suitable for university students, teachers, and scientists interested in fractal theory and its applications.