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The Fractal Geometry of Nature

2021-07-16
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Release : 2021-07-16
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Kind : eBook
Book Rating : 410/5 ( reviews)

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Book Synopsis The Fractal Geometry of Nature by : Benoit Mandelbrot

Download or read book The Fractal Geometry of Nature written by Benoit Mandelbrot. This book was released on 2021-07-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Measure, Topology, and Fractal Geometry

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 340/5 ( reviews)

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Book Synopsis Measure, Topology, and Fractal Geometry by : Gerald A. Edgar

Download or read book Measure, Topology, and Fractal Geometry written by Gerald A. Edgar. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Geometry of Fractal Sets

1985 Mathematics
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Release : 1985
Genre : Mathematics
Kind : eBook
Book Rating : 052/5 ( reviews)

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Book Synopsis The Geometry of Fractal Sets by : K. J. Falconer

Download or read book The Geometry of Fractal Sets written by K. J. Falconer. This book was released on 1985. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ergodic Theory and Fractal Geometry

2014-08-08 Mathematics
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Release : 2014-08-08
Genre : Mathematics
Kind : eBook
Book Rating : 346/5 ( reviews)

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Book Synopsis Ergodic Theory and Fractal Geometry by : Hillel Furstenberg

Download or read book Ergodic Theory and Fractal Geometry written by Hillel Furstenberg. This book was released on 2014-08-08. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zooming-in process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A co-publication of the AMS and CBMS.

Viewpoints

2011-07-05 Mathematics
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Release : 2011-07-05
Genre : Mathematics
Kind : eBook
Book Rating : 05X/5 ( reviews)

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Book Synopsis Viewpoints by : Marc Frantz

Download or read book Viewpoints written by Marc Frantz. This book was released on 2011-07-05. Available in PDF, EPUB and Kindle. Book excerpt: An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)

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