
Fractal Worlds
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Content
- Cover
- Half Title
- Title
- Copyright
- Contents
- Foreword
- Introduction
- 1 What is the shape of the world aroundus?
- 1.1 Types of symmetries
- 1.2 Symmetry under magnification
- 1.3 The Sierpinski gasket
- 1.4 Fractals with memory
- 1.5 Self-affine fractals
- 1.6 Nonlinear fractals
- 1.7 Random fractals
- 1.8 Some non-fractals
- 1.9 Physical world examples
- 2 Self-similarity in geometry
- 2.1 A simple way to grow fractals
- 2.2 Some classical fractals
- 2.3 Fractal trees and ferns
- 2.4 Fractal spirals
- 2.5 IFS with memory
- 2.6 Random rendering of fractal images
- 2.7 Circle inversion fractals
- 2.8 Random fractals
- 2.9 And flavors stranger still
- 3 Self-similarity in the wild
- 3.1 MathWorld vs. PhysicalWorld
- 3.2 A foreshadowing of fractal dimension
- 3.3 Coastlines, mountains, and rivers
- 3.4 How (and why) the lungs are fractal
- 3.5 Power laws
- 3.6 Forests and trees
- 3.7 Our complex hearts
- 3.8 Metabolic rates
- 3.9 Fractals and DNA
- 3.10 How planets grow
- 3.11 Reversals of the Earth's magnetic field
- 3.12 The distribution of galaxies
- 3.13 Is this all?
- 4 Manufactured fractals
- 4.1 Chemical mixers
- 4.2 Capacitors
- 4.3 Wide-band antennas
- 4.4 Invisibility cloaks
- 4.5 Fractal metamaterials
- 4.6 Internet infrastructure
- 4.7 Music
- 4.8 Literature
- 4.9 Visual art
- 4.10 Building fractals
- 5 The Mandelbrot set: infinite complexity from a simple formula
- 5.1 Some pictures
- 5.2 The algorithm
- 5.3 Julia sets
- 5.4 The Mandelbrot set
- 5.5 Other Mandelbrot sets
- 5.6 The universality of the Mandelbrot set
- 5.7 The Mandelbrot set in four dimensions
- 5.8 Unanswered questions
- 6 Quantifying fractals: What is fractal dimension?
- 6.1 Similarity dimension
- 6.2 Box-counting dimension
- 6.3 Mass dimension
- 6.4 Random, with memory, and nonlinear
- 6.5 Dimension rules
- 6.6 Are unearthly dimensions of earthly use?
- 6.7 A speculation about dimensions
- 7 Further developments
- 7.1 Driven IFS
- 7.2 Driven IFS and synchronization
- 7.3 Multifractals from IFS
- 7.4 Applications of multifractals
- 7.5 Fractals and stories, again
- 8 Valediction
- A: A look under the hood:Some technical notes
- B: Solutions ti the problems
- References
- Acknowledgments
- Figure credits
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- X
- Y
- Z
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