Fractal Geometry And Analysis
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| Author | : Gerald A. Edgar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 252 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475741340 |
From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1
| Author | : Christopher J. Bishop |
| Publisher | : Cambridge University Press |
| Total Pages | : 415 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 1107134110 |
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
| Author | : Michel L. Lapidus |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 583 |
| Release | : 2012-09-20 |
| Genre | : Mathematics |
| ISBN | : 1461421764 |
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.
| Author | : Benoit Mandelbrot |
| Publisher | : Echo Point Books & Media, LLC |
| Total Pages | : 0 |
| Release | : 2021-07-16 |
| Genre | : |
| ISBN | : 9781648370410 |
Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.
| Author | : Nancy D. Lorimer |
| Publisher | : |
| Total Pages | : 52 |
| Release | : 1994 |
| Genre | : Forests and forestry |
| ISBN | : |
| Author | : Kenneth Falconer |
| Publisher | : OUP Oxford |
| Total Pages | : 153 |
| Release | : 2013-09-26 |
| Genre | : Mathematics |
| ISBN | : 0191663441 |
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.
| Author | : K. J. Falconer |
| Publisher | : Cambridge University Press |
| Total Pages | : 184 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : 9780521337052 |
A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.
| Author | : Martin J. Turner |
| Publisher | : Academic Press |
| Total Pages | : 352 |
| Release | : 1998-06-23 |
| Genre | : Computers |
| ISBN | : 9780127039701 |
This book is concerned with the theory and application of fractal geometry in digital imaging. Throughout the book, a series of new approaches to defining fractals are illustrated, such as the analysis of the fractal power spectrum and the use of fractional differentials. Several new algorithms and applications are also discussed and applied to real life images. Fractal Geometry in Digital imaging will appeal to postgraduates, researchers and practitioners in image processing, mathematics and computing, information technology and engineering.
| Author | : Santo Banerjee |
| Publisher | : CRC Press |
| Total Pages | : 0 |
| Release | : 2024-10-08 |
| Genre | : Mathematics |
| ISBN | : 9781032138732 |
The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.
| Author | : Jun Kigami |
| Publisher | : Cambridge University Press |
| Total Pages | : 238 |
| Release | : 2001-06-07 |
| Genre | : Mathematics |
| ISBN | : 0521793211 |
This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.
