MTU Cork Library Catalogue

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Fractals, chaos, power laws : minutes from an infinite paradise / Manfred Schroeder.

By: Schroeder, M. R. (Manfred Robert), 1926-.
Material type: materialTypeLabelBookPublisher: New York : W.H. Freeman, 1991Description: xviii, 429 p., [8] p. of plates : ill. (some col.) ; 25 cm.ISBN: 0716721368 .Subject(s): Symmetry (Physics)DDC classification: 530.1
Contents:
Introduction -- Similarity and dissimilarity -- Self similarity - discrete, continuous, strict and otherwise -- Power laws: endless sources of self-similarity -- Noises: white, pink, brown and black -- Brownian motion, gambling losses and intergalactic voids: random fractals par excellence -- Cantor sets: self-similarity and arithmetic dust -- Fractals in higher dimensions and a digital sundial -- Multifractals: intimately intertwined fractals -- Some practical fractals and their measurement -- Iteration, strange mappings and a billion digits for PI -- A self-similar sequence, the logistic parabola and symbolic dynamics -- A forbidden symmetry, Fibonacci's rabbits and a new state of matter -- Periodic and quasiperiodic structures in space -- the route to spatial chaos -- Percolation: from forest fires to epidemics -- Phase transitions and renormalization -- Cellular automata.
Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
General Lending MTU Bishopstown Library Lending 530.1 (Browse shelf(Opens below)) 1 Available 00015230
General Lending MTU Bishopstown Library Lending 530.1 (Browse shelf(Opens below)) 1 Available 00030503
Total holds: 0

Includes bibliographical references (pages 395-410) and indexes.

Introduction -- Similarity and dissimilarity -- Self similarity - discrete, continuous, strict and otherwise -- Power laws: endless sources of self-similarity -- Noises: white, pink, brown and black -- Brownian motion, gambling losses and intergalactic voids: random fractals par excellence -- Cantor sets: self-similarity and arithmetic dust -- Fractals in higher dimensions and a digital sundial -- Multifractals: intimately intertwined fractals -- Some practical fractals and their measurement -- Iteration, strange mappings and a billion digits for PI -- A self-similar sequence, the logistic parabola and symbolic dynamics -- A forbidden symmetry, Fibonacci's rabbits and a new state of matter -- Periodic and quasiperiodic structures in space -- the route to spatial chaos -- Percolation: from forest fires to epidemics -- Phase transitions and renormalization -- Cellular automata.

Reviews provided by Syndetics

Publishers Weekly Review

Readers of James Gleick's 1989 bestseller, Chaos, The Making of a New Science, will find the revolution predicted there in full swing in this advanced look at ``self-similarity, ' ' one of chaos theory's most appealing applications. Self-similarity in computer graphics yields the awesome fractal mountain patterns that have made chaos a visible theory for many nonmathematicians. Readers with good command of calculus and some physics will appreciate how far chaos theory has penetrated theoretical physics, biology and the practice of research as described in puns, illustrations and puzzles by this 20th-century Lewis Carroll. Without those skills, however, readers may stand like Alice before a small door that opens on strange new wonders of the physical world, the extended horizons of number theory and advanced math recreation. Schroeder is a professor of physics at Goettingen University in Germany. (Apr.) (c) Copyright PWxyz, LLC. All rights reserved

CHOICE Review

During the past few decades, new developments in mathematics and the physical sciences have combined to reveal unexpected patterns in nature. In this entertaining survey, Schroeder has managed to touch upon an extraordinary variety of such developments. A basic theme throughout the text is self-similarity, the symmetry that underlies such topics of recent fundamental research as fractals, chaos, and the renormalization group. The scope of the applications described here is impressive music, forest fires, investment strategies, and the reproductive habits of rabbits are all shown to have common mathematical bases. As the subtitle "Minutes from an Infinite Paradise" implies, the expositions are not meant to be complete or rigorous, but they convey nicely the spirit of the current activities for beginners and scholars alike. The subject and author indexes are excellent and numerous references to the primary literature will satisfy those who wish to pursue these subjects further. All levels of interested readers.-J. U. Trefny, Colorado School of Mines

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