Author | Barnsley, Michael F. author |
---|---|
Title | The Science of Fractal Images [electronic resource] / by Michael F. Barnsley, Robert L. Devaney, Benoit B. Mandelbrot, Heinz-Otto Peitgen, Dietmar Saupe, Richard F. Voss ; edited by Heinz-Otto Peitgen, Dietmar Saupe |
Imprint | New York, NY : Springer New York, 1988 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3784-6 |
Descript | XIV, 312 p. online resource |
1 Fractals in nature: From characterization to simulation -- 1.1 Visual introduction to fractals: Coastlines, mountains and clouds -- 1.2 Fractals in nature: A brief survey from aggregation to music -- 1.3 Mathematical models: Fractional Brownian motion -- 1.4 Algorithms: Approximating fBm on a finite grid -- 1.5 Laputa: A concluding tale -- 1.6 Mathematical details and formalism -- 2 Algorithms for random fractals -- 2.1 Introduction -- 2.2 First case study: One-dimensional Brownian motion -- 2.3 Fractional Brownian motion : Approximation by spatial methods -- 2.4 Fractional Brownian motion : Approximation by spectral synthesis -- 2.5 Extensions to higher dimensions -- 2.6 Generalized stochastic subdivision and spectral synthesis of ocean waves -- 2.7 Computer graphics for smooth and fractal surfaces -- Color plates and captions -- 2.8 Random variables and random functions -- 3 Fractal patterns arising in chaotic dynamical systems -- 3.1 Introduction -- 3.2 Chaotic dynamical systems -- 3.3 Complex dynamical systems -- 4 Fantastic deterministic fractals -- 4.1 Introduction -- 4.2 The quadratic family -- 4.3 Generalizations and extensions -- 5 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 -- 5.4 The computation of images from IFS codes -- 5.5 Determination of IFS codes: The Collage Theorem -- 5.6 Demonstrations -- A 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 displacementsโ 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 โcreasedโ 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 โThe Fractal Geometry of Natureโ -- B An eye for fractals -- Dietmar Saupe -- C 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 Exploring the Mandelbrot set -- B An eye for fractals -- Yuval Fisher -- D.1 Bounding the distance to M -- D.2 Finding disks in the interior of M -- D.3 Connected Julia sets