Fractals: A Very Short Introduction

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Overview

From the contours of coastlines to the outlines of clouds, and the branching of trees, fractal shapes can be found everywhere in nature. In this Very Short Introduction, Kenneth Falconer explains the basic concepts of fractal geometry, which produced a revolution in our mathematical understanding of patterns in the twentieth century, and explores the wide range of applications in science, and in aspects of economics.

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Fractals: A Very Short Introduction

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Overview

From the contours of coastlines to the outlines of clouds, and the branching of trees, fractal shapes can be found everywhere in nature. In this Very Short Introduction, Kenneth Falconer explains the basic concepts of fractal geometry, which produced a revolution in our mathematical understanding of patterns in the twentieth century, and explores the wide range of applications in science, and in aspects of economics.

About the Series:
Oxford's Very Short Introductions series offers concise and original introductions to a wide range of subjects—from Islam to Sociology, Politics to Classics, Literary Theory to History, and Archaeology to the Bible. Not simply a textbook of definitions, each volume in this series provides trenchant and provocative—yet always balanced and complete—discussions of the central issues in a given discipline or field. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how the subject has developed and how it has influenced society. Eventually, the series will encompass every major academic discipline, offering all students an accessible and abundant reference library. Whatever the area of study that one deems important or appealing, whatever the topic that fascinates the general reader, the Very Short Introductions series has a handy and affordable guide that will likely prove indispensable.

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Editorial Reviews

From the Publisher
"If you are not familiar with the mathematical basis of fractals, the basic history of the development of the field and how they can be used to describe many natural processes, then this book will serve as an effective primer." —MAA Reviews

"Anyone intrigued by gorgeous pictures of fractals seen in other books or online may turn here to learn about the mathematics behind them...The present book includes references to important papers, some background history, and fascinating applications." —CHOICE

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Product Details

  • ISBN-13: 9780199675982
  • Publisher: Oxford University Press
  • Publication date: 12/1/2013
  • Series: Very Short Introductions Series
  • Pages: 144
  • Sales rank: 586,044
  • Product dimensions: 4.30 (w) x 6.70 (h) x 0.40 (d)

Meet the Author

Kenneth Falconer, Professor of Pure Mathematics, University of St Andrews

Kenneth Falconer is Professor of Pure Mathematics at St Andrews University. He has published many papers on fractal geometry, and three books on the topic, including Fractal Geometry: Mathematical Foundations and Applications (Wiley-Blackwell).

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Table of Contents

Preface
1. The fractal concept
2. Self-similarity
3. Fractal dimension
4. Julia sets and the Mandelbrot set
5. Random walks and Brownian motion
6. Fractals in the real world
7. A little history
Further reading

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Customer Reviews

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Sort by: Showing 1 Customer Reviews
  • Posted December 30, 2013

    more from this reviewer

    We¿ve all come across images of fractals: almost infinitely intr

    We’ve all come across images of fractals: almost infinitely intricate and complex visual patterns that challenge almost all of our intuitions about geometry. Fractal lines are oftentimes infinitely long, yet they are contained within very well defined areas. The same goes for other measures of fractals in higher dimensions: area, volume, etc., In fact, the very notion of dimension as we normally understand it loses meaning when applied to fractals. 




    This short book tries to give a very intuitive and easy-to-follow introduction to fractals. It starts by examining some prototypical fractal sets that are relatively easy to construct, at least in principle. Fractals and fractal-related notions actually have a pretty long history, but they had only become popular in the last few decades. This is largely thanks to the advent of modern computers, and the ability to visualize many of the more interesting fractals for the first time. 




    Fractals are not just pretty pictures. They are based on some really profound and intricate mathematical concepts. What makes fractals from the mathematical viewpoint particularly fascinating is that the rules that are required for describing a fractal are seemingly very simple, and yet in order to understand the full intricacy of a fractal requires some exceedingly complex higher mathematics. To this book’s credit it tries to explain some of the richness of this mathematics, without, of course, going into any detail. To fully appreciate this material the reader should be able to understand at least some more abstract mathematical concepts – such as imaginary and complex numbers – but other than that a curious mind and a willingness to be intellectually engaged should be sufficient. 




    The book also covers several applications of fractals – in nature, science and finance to name a few. These examples illustrate that fractals, far from being just an idle abstract curiosity, are actually a very useful and powerful tool for the understanding of many aspects of the world around us. 




    The book is very elegantly written, and it is very accessible and a pleasure to read. This is perhaps one of the best examples of popular math book that I’ve ever come across. 

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