Fractal Geometry: Mathematical Foundations and Applications

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9780471922872: Fractal Geometry: Mathematical Foundations and Applications
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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.

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Fractal Geometry Mathematical Foundations and Applications Kenneth Falconer, School of Mathematics, University of Bristol, UK This book provides an accessible treatment of the mathematics of fractals and their dimensions. It is aimed at those wanting to use fractals in their own areas of mathematics or science. The first part of the book covers the general theory of fractals and their geometry. Results are stated precisely, but technical measure theoretic ideas are avoided and difficult proofs are sketched or omitted. The second part contains a variety of examples and applications in mathematics and physics.

About the Author:

About the author Kenneth Falconer took his MA and PhD degrees at Cambridge University and was Research Fellow at Corpus Christi College, Cambridge, from 1977 to 1980. He then joined Bristol University where he is now a Reader. He was visiting Professor at Oregon State University, USA, in 1985-6 and has lectured widely in Britain and abroad. He has published The Geometry of Fractal Sets (Cambridge University Press 1985) as well as more than 40 research papers, largely on fractals, geometric measure theory, and the geometry of convex sets. 'To be convinced that fractal geometry is not mere pretty pictures, but solid and fascinating mathematics, look no further.' Ian Stewart, New Scientist

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