Introducing Fractals

2014-06-05
Introducing Fractals

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  • Author: Nigel Lesmoir-Gordon
  • Publisher: Icon Books Ltd
  • ISBN: 1848317832
  • Category : Mathematics
  • Languages : en
  • Pages : 429

Fractals are the geometry of the natural world. They're about the broken, wrinkled, wiggly world- the uneven shapes of nature, unlike the idealised forms of Euclidean geometry. We see fractals everywhere; indeed, we are fractals ourselves. Fractal geometry is an extension of classical geometry which can make precise models of physical structures, from ferns to galaxies. It can describe the shape of a cloud as precisely as an architect can describe a house. Introducing Fractals traces the historical development of this mathematical discipline, explores its descriptive powers in the natural world, and then looks at the applications and the implications of the discoveries it has made. As John Archibald Wheeler, protégé of Niels Bohr, friend of Albert Einstein and mentor of Richard Feynman has said, 'No one will be considered scientifically literate tomorrow, who is not familiar with fractals.'

Introducing Fractal Geometry

2006
Introducing Fractal Geometry

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  • Author: Nigel Lesmoir-Gordon
  • Publisher: Totem Books
  • ISBN: 9781840467130
  • Category : Fractals
  • Languages : en
  • Pages : 0

This title is now available in a new format. Refer to Fractals: A Graphic Guide 9781848310872.

Fractals: A Very Short Introduction

2013-09-26
Fractals: A Very Short Introduction

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  • Author: Kenneth Falconer
  • Publisher: OUP Oxford
  • ISBN: 019166345X
  • Category : Mathematics
  • Languages : en
  • Pages : 177

Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Fractal Geometry in Human Geography and Planning

2024-08-27
Fractal Geometry in Human Geography and Planning

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  • Author: Cécile Tannier
  • Publisher: John Wiley & Sons
  • ISBN: 1789451590
  • Category : Social Science
  • Languages : en
  • Pages : 372

The aim of this book is to provide an overview of the concepts and methods used in fractal analysis and modeling in order to study the spatial distribution of human settlements. The main concepts and mathematical tools are reviewed, and emphasis is placed on the practical benefits of their application and the pitfalls to be avoided when using them. The first part of the book is devoted to the basic concepts and geometric reference figures required for fractal analysis in human geography. In the second part, the principles of four major families of analysis methods are explained in detail: fractal analyses of point sequences, fractal methods for morphological delineation of urban agglomerations, multifractal analyses and cross scale signatures. The third part of the book is devoted to applications of fractal geometry in urban and regional planning.

Fractal Geometry

2014-02-03
Fractal Geometry

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  • Author: Kenneth Falconer
  • Publisher: John Wiley & Sons
  • ISBN: 111994239X
  • Category : Mathematics
  • Languages : en
  • Pages : 404

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals Carefully explains each topic using illustrative examples and diagrams Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics Features a wide range of exercises, enabling readers to consolidate their understanding Supported by a website with solutions to exercises and additional material www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)

Chaos and Fractals

2012-08-09
Chaos and Fractals

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  • Author: David P. Feldman
  • Publisher: Oxford University Press, USA
  • ISBN: 0199566445
  • Category : Mathematics
  • Languages : en
  • Pages : 432

For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.

Fractals: A Very Short Introduction

2013-09-26
Fractals: A Very Short Introduction

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  • Author: Kenneth Falconer
  • Publisher: OUP Oxford
  • ISBN: 0191663441
  • Category : Mathematics
  • Languages : en
  • Pages : 153

Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

The Colours of Infinity

2010-10-20
The Colours of Infinity

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  • Author: Nigel Lesmoir-Gordon
  • Publisher: Springer Science & Business Media
  • ISBN: 1849964866
  • Category : Mathematics
  • Languages : en
  • Pages : 218

A geometry able to include mountains and clouds now exists. I put it together in 1975, but of course it incorporates numerous pieces that have been around for a very long time. Like everything in science, this new geometry has very, very deep and long roots. Benoît B. Mandelbrot Introduction This enhanced and expanded edition of THE COLOURS OF INFINITY features an additional chapter on the money markets by the fractal master himself, Professor Benoît Mandelbrot. The DVD of the film associated with this book has been re-mastered especially for this edition with exquisite new fractal animations, which will take your breath away! Driven by the curious enthusiasm that engulfs many fractalistas, in 1994, Nigel Lesmoir-Gordon overcame enormous obstacles to raise the finance for, then shoot and edit the groundbreaking TV documentary from which this book takes its name. The film has been transmitted on TV channels in over fifty countries around the world. This book is not just a celebration of the discovery of the Mandelbrot set, it also brings fractal geometry up to date with a gathering of the thoughts and enthusiasms of the foremost writers and researchers in the field. As Ian Stewart makes clear in the opening chapter, there were antecedents for fractal geometry before 1975 when Mandelbrot gave the subject its name and began to develop the underlying theory.

The Grapes of Math

2014-06-10
The Grapes of Math

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  • Author: Alex Bellos
  • Publisher: Simon and Schuster
  • ISBN: 1451640129
  • Category : Mathematics
  • Languages : en
  • Pages : 352

From triangles, rotations and power laws, to cones, curves and the dreaded calculus, Alex takes you on a journey of mathematical discovery with his signature wit and limitless enthusiasm. He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

Fractals for the Classroom

2013-03-09
Fractals for the Classroom

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  • Author: Heinz-Otto Peitgen
  • Publisher: Springer Science & Business Media
  • ISBN: 1475721722
  • Category : Mathematics
  • Languages : en
  • Pages : 468

Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating insights for the classroom teacher and integrates illustrations from a wide variety of applications with an enjoyable text to help bring the concepts alive and make them understandable to the average reader. This book will have a tremendous impact upon teachers, students, and the mathematics education of the general public. With the forthcoming companion materials, including four books on strategic classroom activities and lessons with interactive computer software, this package will be unparalleled.