Muutke küpsiste eelistusi

Fractal Worlds: Grown, Built, and Imagined [Pehme köide]

4.56/5 (32 hinnangut Goodreads-ist)
,
  • Formaat: Paperback / softback, 544 pages, kõrgus x laius x paksus: 235x156x28 mm, kaal: 676 g, 328 b-w illus.
  • Ilmumisaeg: 07-Jun-2016
  • Kirjastus: Yale University Press
  • ISBN-10: 030019787X
  • ISBN-13: 9780300197877
Teised raamatud teemal:
  • Pehme köide
  • Hind: 25,32 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Tavahind: 29,79 €
  • Säästad 15%
  • Raamatu kohalejõudmiseks kirjastusest kulub orienteeruvalt 2-4 nädalat
  • Kogus:
  • Lisa ostukorvi
  • Tasuta tarne
  • Tellimisaeg 2-4 nädalat
  • Lisa soovinimekirja
Fractal Worlds: Grown, Built, and ImaginedSuurem pilt
  • Formaat: Paperback / softback, 544 pages, kõrgus x laius x paksus: 235x156x28 mm, kaal: 676 g, 328 b-w illus.
  • Ilmumisaeg: 07-Jun-2016
  • Kirjastus: Yale University Press
  • ISBN-10: 030019787X
  • ISBN-13: 9780300197877
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780300197877.html
Märksõnad:
Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame—a close collaborator with Benoit Mandelbrot, the founder of fractal geometry—and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into less-known areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching.

Arvustused

Highly readable but detailed introduction to fractal geometry. . . enthusiastic, varied, and thought-provoking. Gavin M. Abernathy, London Mathematical Society Journal 

Won an Honorable Mention in the Mathematics category for the 2017 American Publishers Awards for Professional & Scholarly Excellence (PROSE).

Selected by Choice magazine as one of the Top 75 Community College Titles for 2016

Fractal Worlds portrays math as math lovers know it: a beautiful garden, a place of curiosity and delight, a tribute to human creativity and the wonders of nature.Steven Strogatz, author of Sync and The Joy of x

Fractal Worlds is a cornucopia of all things fractal. Simultaneously rigorous and gentle, it engages the reader in orderly, yet wildly imaginative, musings. An instant classic.David Peak, Utah State University

Frame and Urry give us the ultimate perusing experience of fractal marvels as a far-reaching string of luminous gems encircling literature, art, science, and nature.Joseph Mazur, author of Fluke: The Math and Myth of Coincidences

Fractal Worlds can be appreciated at many levels. Experts and newcomers alike will discover fresh gems from the universe of fractals, their science, mathematics, and art.Kenneth Falconer, author of Fractal Geometry: Mathematical Foundations and Applications Fractal Worlds portrays math as math lovers know it: a beautiful garden, a place of curiosity and delight, a tribute to human creativity and the wonders of nature.Steven Strogatz, author of Sync and The Joy of x -- Steven Strogatz Fractal Worlds is a cornucopia of all things fractal. Simultaneously rigorous and gentle, it engages the reader in orderly, yet wildly imaginative, musings. An instant classic.David Peak, Utah State University -- David Peak Frame and Urry give us the ultimate perusing experience of fractal marvels as a far-reaching string of luminous gems encircling literature, art, science, and nature.Joseph Mazur, author of Fluke: The Math and Myth of Coincidences -- Joseph Mazur Fractal Worlds can be appreciated at many levels. Experts and newcomers alike will discover fresh gems from the universe of fractals, their science, mathematics, and art.Kenneth Falconer, author of Fractal Geometry: Mathematical Foundations and Applications -- Kenneth Falconer Won an Honorable Mention in the Mathematics category for the 2017 American Publishers Awards for Professional & Scholarly Excellence (PROSE). -- PROSE * PROSE *

Foreword ix
Steven Strogatz
Introduction xi
1 What is the shape of the world around us?
1(14)
1.1 Types of symmetries
1(1)
1.2 Symmetry under magnification
2(2)
1.3 The Sierpinski gasket
4(1)
1.4 Fractals with memory
5(1)
1.5 Self-affine fractals
6(1)
1.6 Nonlinear fractals
6(1)
1.7 Random fractals
7(1)
1.8 Some non-fractals
8(2)
1.9 Physical world examples
10(5)
2 Self-similarity in geometry
15(40)
2.1 A simple way to grow fractals
15(6)
2.2 Some classical fractals
21(8)
2.3 Fractal trees and ferns
29(4)
2.4 Fractal spirals
33(1)
2.5 IFS with memory
34(8)
2.6 Random rendering of fractal images
42(4)
2.7 Circle inversion fractals
46(5)
2.8 Random fractals
51(2)
2.9 And flavors stranger still
53(2)
3 Self-similarity in the wild
55(34)
3.1 MathWorld vs. PhysicalWorld
56(1)
3.2 A foreshadowing of fractal dimension
56(2)
3.3 Coastlines, mountains, and rivers
58(6)
3.4 How (and why) the lungs are fractal
64(3)
3.5 Power laws
67(3)
3.6 Forests and trees
70(1)
3.7 Our complex hearts
71(2)
3.8 Metabolic rates
73(2)
3.9 Fractals and DNA
75(5)
3.10 How planets grow
80(2)
3.11 Reversals of the Earth's magnetic field
82(1)
3.12 The distribution of galaxies
83(2)
3.13 Is this all?
85(4)
4 Manufactured fractals
89(40)
4.1 Chemical mixers
90(1)
4.2 Capacitors
91(1)
4.3 Wide-band antennas
92(2)
4.4 Invisibility cloaks
94(1)
4.5 Fractal metamaterials
95(2)
4.6 Internet infrastructure
97(2)
4.7 Music
99(6)
4.8 Literature
105(14)
4.9 Visual art
119(9)
4.10 Building fractals
128(1)
5 The Mandelbrot set: infinite complexity from a simple formula
129(30)
5.1 Some pictures
130(1)
5.2 The algorithm
131(3)
5.3 Julia sets
134(4)
5.4 The Mandelbrot set
138(9)
5.5 Other Mandelbrot sets
147(2)
5.6 The universality of the Mandelbrot set
149(4)
5.7 The Mandelbrot set in four dimensions
153(3)
5.8 Unanswered questions
156(3)
6 Quantifying fractals: What is fractal dimension?
159(46)
6.1 Similarity dimension
160(7)
6.2 Box-counting dimension
167(10)
6.3 Mass dimension
177(2)
6.4 Random, with memory, and nonlinear
179(10)
6.5 Dimension rules
189(7)
6.6 Are unearthly dimensions of earthly use?
196(5)
6.7 A speculation about dimensions
201(4)
7 Further developments
205(44)
7.1 Driven IFS
205(11)
7.2 Driven IFS and synchronization
216(10)
7.3 Multifractals from IFS
226(7)
7.4 Applications of multifractals
233(9)
7.5 Fractals and stories, again
242(7)
8 Valediction
249(4)
A A look under the hood: Some technical notes 253(154)
B Solutions to the problems 407(32)
References 439(52)
Acknowledgments 491(2)
Figure credits 493(2)
Index 495
Michael Frame taught mathematics at Yale University for twenty years. Amelia Urry is a journalist and poet.