Captures some of the mathematical excitement and visual wonder of fractals when they were the Latest New Thing. ( )

Indeholder "Michael F. Barnsley, Robert L. Devaney, Yuval Fisher, Benoit B. Mandelbrot, Michael McGuire, Heinz-Otto Peitgen, Dietmar Saupe, Richard F. Voss: Preface", "Benoit B. Mandelbrot: Foreword. People and events behind the "Science of Fractal Images"", " 0.1 The prehistory of some fractals-to-be: Poincare, Fricke, Klein and Escher", " 0.2 Fractals at IBM", " 0.3 The fractal mountains by R. F. Voss", " 0.4 Old films", " 0.5 Star Trek II", " 0.6 Midpoint displacement in Greek geometry: The Archimedes construction for the parabola", " 0.7 Fractal clouds", " 0.8 Fractal trees", " 0.9 Iteration, yesterday's dry mathematics and today's weird and wonderful new fractal shapes, and the "Geometry Supercomputer Project"", " 0.10 Devaney, Barnsley and the Bremen "Beauty of Fractals"", "1. Richard F. Voss: Fractals in nature. From characterization to simulation", " 1.1 Visual introduction to fractals: Coastlines, mountains and clouds", " 1.1.1 Mathematical monsters: The fractal heritage", " 1.1.2 Fractals and self-similarity", " 1.1.3 An early monster: The von Koch snowflake curve", " 1.1.4 Self-similarity and dimension", " 1.1.5 Statistical self-similarity", " 1.1.6 Mandelbrot landscapes", " 1.1.7 Fractally distributed craters", " 1.1.8 Fractal planet: Brownian motion on a sphere", " 1.1.9 Fractal flakes and clouds", " 1.2 Fractals in nature: A brief survey from aggregation to music.", " 1.2.1 Fractals at large scales", " 1.2.2 Fractals at small scales: Condensing matter", " 1.2.3 Scaling randomness in time: 1/f^beta-noises", " 1.2.4 Fractal music", " 1.3 Mathematical models: Fractional Brownian motion", " 1.3.1 Self-affinity", " 1.3.2 Zerosets", " 1.3.3 Self-affinity in higher dimensions: Mandelbrot land- scapes and clouds", " 1.3.4 Spectral densities for fBm and the spectral exponent beta", " 1.4 Algorithms: Approximating fBm on a finite grid", " 1.4.1 Brownian motion as independent cuts", " 1.4.2 Fast Fourier Transform filtering", " 1.4.3 Random midpoint displacement", " 1.4.4 Successive random additions", " 1.4.5 Weierstrass-Mandelbrot random fractal function", " 1.5 Laputa: A concluding tale", " 1.6 Mathematical details and formalism", " 1.6.1 Fractional Brownian motion", " 1.6.2 Exact and statistical self-similarity", " 1.6.3 Measuring the fractal dimension D", " 1.6.4 Self-affinity", " 1.6.5 The relation of D to H for self-affine fractional Brownian motion", " 1.6.6 Trails of fBm", " 1.6.7 Self-affinity in E dimensions", " 1.6.8 Spectral densities for fBm and the spectral exponent beta", " 1.6.9 Measuring fractal dimensions: Mandelbrot measures", " 1.6.10 Lacunarity", " 1.6.11 Random cuts with H not equal to 1/2: Campbell's theorem", " 1.6.12 FFT filtering in 2 and 3 dimensions", "2. Dietmar Saupe: Algorithms for random fractals", " 2.1 Introduction", " 2.2 First case study: One-dimensional Brownian motion", " 2.2.1 Definitions", " 2.2.2 Integrating white noise", " 2.2.3 Generating Gaussian random numbers", " 2.2.4 Random midpoint displacement method", " 2.2.5 Independent jumps", " 2.3 Fractional Brownian motion: Approximation by spatial methods", " 2.3.1 Definitions", " 2.3.2 Midpoint displacement methods", " 2.3.3 Displacing interpolated points", " 2.4 Fractional Brownian motion: Approximation by spectral synthesis", " 2.4.1 The spectral representation of random functions", " 2.4.2 The spectral exponent beta in fractional Brownian motion", " 2.4.3 The Fourier filtering method", " 2.5 Extensions to higher dimensions", " 2.5.1 Definitions", " 2.5.2 Displacement methods", " 2.5.3 The Fourier filtering method", " 2.6 Generalized stochastic subdivision and spectral synthesis of ocean waves", " 2.7 Computer graphics for smooth and fractal surfaces", " 2.7.1 Top view with color mapped elevations", " 2.7.2 Extended floating horizon method", "Color plates and captions", " 2.7.3 The data and the projection", " 2.7.4 A simple illumination model", " 2.7.5 The rendering", " 2.7.6 Data manipulation", " 2.7.7 Color, anti-aliasing and shadows", " 2.7.8 Data storage considerations", " 2.8 Random variables and random functions", "3. Robert L. Devaney: Fractal patterns arising in chaotic dynamical systems", " 3.1 Introduction", " 3.1.1 Dynamical systems", " 3.1.2 An example from ecology", " 3.1.3 Iteration", " 3.1.4 Orbits", " 3.2 Chaotic dynamical systems", " 3.2.1 Instability: The chaotic set", " 3.2.2 A chaotic set in the plane", " 3.2.3 A chaotic gingerbreadman", " 3.3 Complex dynamical systems", " 3.3.1 Complex maps", " 3.3.2 The Julia set", " 3.3.3 Julia sets as basin boundaries", " 3.3.4 Other Julia sets", " 3.3.5 Exploding Julia sets", " 3.3.6 Intermittency", "4. Heinz-Otto Peitgen: Fantastic deterministic fractals", " 4.1 Introduction", " 4.2 The quadratic family", " 4.2.1 The Mandelbrot set", " 4.2.2 Hunting for Kc in the plane - the role of critical points", " 4.2.3 Level sets", " 4.2.4 Equipotential curves", " 4.2.5 Distance estimators", " 4.2.6 External angles and binary decompositions", " 4.2.7 Mandelbrot set as one-page-dictionary of Julia sets", " 4.3 Generalizations and extensions", " 4.3.1 Newton's Method", " 4.3.2 Sullivan classification", " 4.3.3 The quadratic family revisited", " 4.3.4 Polynomials", " 4.3.5 A special map of degree four", " 4.3.6 Newton's method for real equations", " 4.3.7 Special effects", "5. Michael F. Barnsley: Fractal modelling of real world images", " 5.1 Introduction", " 5.2 Background references and introductory comments", " 5.3 Intuitive introduction to IFS: Chaos and measures", " 5.3.1 The Chaos Game: 'Heads', 'Tails' and 'Side'", " 5.3.2 How two ivy leaves lying on a sheet of paper can specify an affine transformation", " 5.4 The computation of images from IFS codes", " 5.4.1 What an IFS code is", " 5.4.2 The underlying model associated with an IFS code", " 5.4.3 How images are defined from the underlying model", " 5.4.4 The algorithm for computing rendered images", " 5.5 Determination of IFS codes: The Collage Theorem", " 5.6 Demonstrations", " 5.6.1 Clouds", " 5.6.2 Landscape with chimneys and smoke", " 5.6.3 Vegetation", "A. Benoit B. Mandelbrot: Fractal landscapes without creases and with rivers", " A.1 Non-Gaussian and non-random variants of midpoint displacement", " A.1.1 Midpoint displacement constructions for the paraboloids", " A.1.2 Midpoint displacement and systematic fractals: The Takagi fractal curve, its kin, and the related surfaces", " A.1.3 Random midpoint displacements with a sharply non- Gaussian displacements' distribution.", " A.2 Random landscapes without creases", " A.2.1 A classification of subdivision schemes: One may displace the midpoints of either frame wires or of tiles", " A.2.2 Context independence and the 'creased' texture", " A.2.3 A new algorithm using triangular tile midpoint displacement", " A.2.4 A new algorithm using hexagonal tile midpoint displacement", " A.3 Random landscape built on prescribed river networks", " A.3.1 Building on a non-random map made of straight rivers and watersheds, with square drainage basins", " A.3.2 Building on the non-random map shown on the top of Plate 73 of 'The Fractal Geometry of Nature'", "B. Michael McGuire: An eye for fractals", "C. Dietmar Saupe: A unified approach to fractal curves and plants", " C.1 String rewriting systems", " C.2 The von Koch snowflake curve revisited", " C.3 Formal definitions and implementation", "D. Yuval Fisher: Exploring the Mandelbrot set", " D.1 Bounding the distance to M", " D.2 Finding disks in the interior of M", " D.3 Connected Julia sets", "Bibliography", "Index".

En vældig teknisk bog, men også med lidt historie og en masse fif til hvordan man laver de flotte billeder i bogen ( )

Remember the 80's?: MTV, John Hughes, and z(n+1) = z(n)*z(n) + 1.