Fractal Geometry: Mathematical Foundations and Applications [Hardcover]

Kenneth Falconer (Author)

Book Description

Publication Date: March 16, 1990 | ISBN-10: 0471922870 | ISBN-13: 978-0471922872 | Edition: 1

An accessible introduction to fractals, useful as a text or reference. Part I is concerned with the general theory of fractals and their geometry, covering dimensions and their methods of calculation, plus the local form of fractals and their projections and intersections. Part II contains examples of fractals drawn from a wide variety of areas of mathematics and physics, including self-similar and self-affine sets, graphs of functions, examples from number theory and pure mathematics, dynamical systems, Julia sets, random fractals and some physical applications. Also contains many diagrams and illustrative examples, includes computer drawings of fractals, and shows how to produce further drawings for themselves.

Editorial Reviews

Review

"…(the second edition) features new material, additional exercises, notes and references and an extended bibliography…" (Zentralblatt Fur Didatik der Mathematik) --This text refers to an alternate Hardcover edition.

From the Publisher

An accessible introduction to fractals, useful as a text or reference. Part I is concerned with the general theory of fractals and their geometry, covering dimensions and their methods of calculation, plus the local form of fractals and their projections and intersections. Part II contains examples of fractals drawn from a wide variety of areas in mathematics and physics, including self-similar and self-affine sets, graphs of functions, examples from number theory and pure mathematics, dynamical systems, Julia sets, random fractals, and some physical applications. Also contains many diagrams and illustrative examples, includes computer drawings of fractals, and shows how to produce further drawings.

See all Editorial Reviews

Product Details

• Hardcover: 310 pages
• Publisher: John Wiley & Sons; 1 edition (March 16, 1990)
• Language: English
• ISBN-10: 0471922870
• ISBN-13: 978-0471922872
• Product Dimensions: 9.1 x 5.9 x 0.9 inches
• Shipping Weight: 1.2 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #1,593,881 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

22 of 22 people found the following review helpful:

5.0 out of 5 stars Exposes fractal geometry as a real mathematical discipline., April 13, 2000

By 

Bernardo Vargas - See all my reviews

This review is from: Fractal Geometry: Mathematical Foundations and Applications (Hardcover)

I appreciate Falconer's books on fractal geometry because they show the topic as it really is: a whole mathematical discipline on its own right and not just a nice temporary fashion.

It begins introducing basic topological concepts and then proceeds to develop the theory for several possible definitions of fractal dimension, showing the relations between them. Then it explores deeply the local geometry of different kinds of fractal objects, and studies some other geometrical situations, like the pojection of fractals (ever thought of a DIGITAL sundial? Here it is described!).

The book also includes a lot of applications to other areas of mathematics and physics, a great amount of graphics, and much more.

The text is suitable from third year undergraduate school and on. It is a larger but lighter version of "The Geometry of Fractal Sets".

17 of 18 people found the following review helpful:

5.0 out of 5 stars What every student should know about fractals., February 9, 2003

By 

Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

Amazon Verified Purchase

This review is from: Fractal Geometry: Mathematical Foundations and Applications (Hardcover)

Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.

15 of 16 people found the following review helpful:

5.0 out of 5 stars Theoretical as well as practical insight, August 13, 2001

By 

Steve Uhlig (Berlin, Germany) - See all my reviews
(REAL NAME)   

This review is from: Fractal Geometry: Mathematical Foundations and Applications (Paperback)

The first part of the book is essentially of a theoretical nature, with a thorough treatment of fractal geometry at a mathematical point of view. The second part on the other hand provides a flavour of the problems of fractal geometry in practice...so mathematicians as well as people interested in applications only should both find this book interesting. The maths are not easy but quite "understandable" for science undergrads...some notions of calculus or topology would help... but the introduction is excellent and allows anyone to follow the course of the book (but for understanding the proofs a good math background is required).

Excellent for understanding the geometrical properties of fractals.