Fractals: Form, Chance and Dimension

Discover the Hidden Mathematics of Modern Geometry

Fractals, the never-ending geometric-mathematical patterns existing throughout nature, are revealed in the shapes of continents, galaxies, snowflakes, and grains of sand. In this fascinating and seminal volume, renowned pioneering-mathematician Benoit B. Mandelbrot explains his work on fractal geometry, mathematically translating the description of these complex shapes of nature.

Until Mandelbrot developed the concept of fractal geometry in the 1960s and 70s, most mathematicians believed these irregular shapes were too fragmented and amorphous to be described mathematically. Mandelbrot's revolutionary concept brought order to a variety of seemingly unsolvable problems in physics, biology, and financial markets.

Broad in application, this groundbreaking work will inform not just mathematicians, but anyone that appreciates the natural elegance of patterns made manifest. Featuring illustrations of mathematically defined shapes, Mandelbrot describes how geometric patterns relate to every aspect of the physical world around us.

1136543562
Fractals: Form, Chance and Dimension

Discover the Hidden Mathematics of Modern Geometry

Fractals, the never-ending geometric-mathematical patterns existing throughout nature, are revealed in the shapes of continents, galaxies, snowflakes, and grains of sand. In this fascinating and seminal volume, renowned pioneering-mathematician Benoit B. Mandelbrot explains his work on fractal geometry, mathematically translating the description of these complex shapes of nature.

Until Mandelbrot developed the concept of fractal geometry in the 1960s and 70s, most mathematicians believed these irregular shapes were too fragmented and amorphous to be described mathematically. Mandelbrot's revolutionary concept brought order to a variety of seemingly unsolvable problems in physics, biology, and financial markets.

Broad in application, this groundbreaking work will inform not just mathematicians, but anyone that appreciates the natural elegance of patterns made manifest. Featuring illustrations of mathematically defined shapes, Mandelbrot describes how geometric patterns relate to every aspect of the physical world around us.

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Fractals: Form, Chance and Dimension

Fractals: Form, Chance and Dimension

by Benoit B Mandelbrot
Fractals: Form, Chance and Dimension

Fractals: Form, Chance and Dimension

by Benoit B Mandelbrot

Overview

Discover the Hidden Mathematics of Modern Geometry

Fractals, the never-ending geometric-mathematical patterns existing throughout nature, are revealed in the shapes of continents, galaxies, snowflakes, and grains of sand. In this fascinating and seminal volume, renowned pioneering-mathematician Benoit B. Mandelbrot explains his work on fractal geometry, mathematically translating the description of these complex shapes of nature.

Until Mandelbrot developed the concept of fractal geometry in the 1960s and 70s, most mathematicians believed these irregular shapes were too fragmented and amorphous to be described mathematically. Mandelbrot's revolutionary concept brought order to a variety of seemingly unsolvable problems in physics, biology, and financial markets.

Broad in application, this groundbreaking work will inform not just mathematicians, but anyone that appreciates the natural elegance of patterns made manifest. Featuring illustrations of mathematically defined shapes, Mandelbrot describes how geometric patterns relate to every aspect of the physical world around us.

Product Details

ISBN-13: 9781635619027
Publisher: Echo Point Books & Media
Publication date: 02/25/2020
Edition description: Reprint ed.
Pages: 384
Product dimensions: 7.50(w) x 9.25(h) x 0.79(d)

Table of Contents

LIST OF PLATES AND PATTERNS

I. INTRODUCTION

goals ♦ etymology of “fractal” ♦ J. Perrin on irregularity and fragmentation in Nature ♦ from Perrin through Wiener ♦ the fractal palace: museum and toolshed ♦ multiple facets of dimension; definition of fractals ♦ spatial homogeneity and self similarity ♦ limitations of topology in the study of form ♦ physical dimension ♦ many different dimensions implicit in a ball of thread ♦ of notions that are new, but ♦ this Essay mixes styles: is semipopular and scholarly ♦ the role of graphics ♦ points of logistics

II. HOW LONG IS THE COAST OF BRITAIN?

III. USES OF NONCONSTRAINED CHANCE

IV. FRACTAL EVENTS AND NOISES

V. FRACTAL CLUSTERS OF STELLAR MATTER

VI. TURBULENCE, INTERMITTENCY AND CURDLING

VII. METEORITES, MOON CRATERS AND SOAP

VIII. USES OF SELF CONSTRAINED CHANCE

IX. FRACTIONAL BROWNIAN FACETS OF RIVERS, RELIEF, AND TURBULENCE

X. MISCELLANY

XL BIOGRAPHICAL AND HISTORICAL SKETCHES

XII. MATHEMATICAL LEXICON & ADDENDA

BIBLIOGRAPHY

ACKNOWLEDGMENTS

INDEX

INDEX OF SELECTED DIMENSIONS

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