Introducing Fractals Introducing Fractals

Name: Introducing Fractals Introducing Fractals | A Graphic Guide
Brand: Icon Books
Price: 4.99 EUR
Availability: OnlineOnly

A Graphic Guide

Nigel Lesmoir-Gordon Will Rood(Autor*in)

Icon Books (Verlag)

Erschienen am 5. Juni 2014

176 Seiten

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978-1-84831-783-3 (ISBN)

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Inhalt

Intro
Title Page
Copyright
Contents
Why Do Fractals Matter?
A Smooth World or a Rough One?
The Texture of Reality
The Origins of Fractals
Classical Geometry
The Calculus
The Paradox of Infinitesimals
Effects of Calculus
The First Fractal
Explaining Numbers
Firm Foundations and Sets
What Are Sets?
Cantor and the Continuum
The Cantor Set
Peano's Space-Filling Curve
Topological and Fractal Dimension
Self-Similarity
The Koch Curve
Similarity Dimension
Similarity and Fractal Dimension
Measuring Fractal Dimension
Lewis Richardson
How Long is a Coastline?
The Sierpinski Gasket
The Chaos Game
Strange Attractor
Pascal's Triangle
Basins of Attraction
Poincaré and Non-Linearity
Malthus and Population Growth
Negative Feedback
The Logistic Equation
Iteration
Video Feedback
Robert May and the Verhulst Model
Bifurcation Points
The Period-Doubling Cascade
The Fig Tree
Chaos Theory and Fractals
The Feigenbaum Constant
Real Numbers, Other Numbers
Complex Numbers
The Complex Plane
Gaston Julia and Pierre Fatou
Benoît Mandelbrot
Uncle Szolem
A Practical Education
The Shape of Things
The Wiles of Bourbaki
On the Run Again
The More the Merrier
Emerging Patterns
Fractals in Practice
Bad Noise
Fractal Errors
A General Principle Emerges
The Simplest Possible Transformation
Two Types of Julia Sets
A Map of Julia Sets
A Whole New World
Simple Rules, Complex Behaviour
Newton's Law and Chaos
Let's Admit - It is Complicated .
Phase Transitions
Hazy Areas of Calculation
The Mathematics of Wrinkles
Natural Templates
Forest Fires: the Fractal Boundary
More Phase Transitions
Electro-plated Fractals
Viscous Fingering
Growth by Aggregation
Brownian Motion and the Quantum World
Dimensional Magic
The Three-Quarter Power Law
The Mysterious Brain
Knowing the Mind of God?
Fractals and Medical Research
Viruses and Bacteria
AIDS
Detecting Cancer
Women at Risk
Bubbly Bones and Breaks
Fractal Beats
Practical Solutions
Striking Oil
The Spring is Sprung
Stress Loadings
Detection
Fractal Ecology
Orchid Fractals and Crowds
Olbers' Paradox
The Great Wall
The Big Bang
Cosmic Connections
How Do We See?
Fractal Image Compression
Affine Transformations
Morphogenesis
Satellites
The Money Markets
What Are the Rules?
Market Self-Affinity
Generators
Beyond Portfolio Theory
Multifractals
Fractals in Art: Mandalas
Decorative Patterns: Self-Similarity
Scaling and Repetition
Cues in the Landscape
Fractals in Music
Dysfunction in Modern Architecture
Organic Architecture
Fractal Traditions
Strength in the Details
Fracology
Quo Vadis?
Not Everyone Agrees .
The Special Talent of Mandelbrot
The Order Is Out There
Further Reading
Acknowledgements
Biographies
Index

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