7 edition of **A random walk through fractal dimensions** found in the catalog.

- 49 Want to read
- 15 Currently reading

Published
**1994**
by VCH in Weinheim, New York
.

Written in English

- Fractals.

**Edition Notes**

Includes bibliographical references (p. [411]-415) and index.

Statement | Brian H. Kaye. |

Classifications | |
---|---|

LC Classifications | QA614.86 .K38 1994 |

The Physical Object | |

Pagination | xxv, 427 p. : |

Number of Pages | 427 |

ID Numbers | |

Open Library | OL1089258M |

ISBN 10 | 3527290788, 1560818182 |

LC Control Number | 94013337 |

Random walks on fractals have an added interest: random walk trails (e.g. sample paths of Brownian motion) are them- selves fractal in general, and interesting kinds of behavior emerge when they occur on fractal structures, in the form of scaling laws. In the case of random fractals, one has a "random Cited by: /Algebra & Trigonometry/A Random Walk Through Fractal Dimensions 2nd ed - B. Kaye (Wiley-VCH, )

A tale of two fractals. This book is devoted to a phenomenon of fractal sets, or simply fractals. Topics covered includes: Sierpinski gasket, Harmonic functions on Sierpinski gasket, Applications of generalized numerical systems, Apollonian Gasket, Arithmetic properties of Apollonian gaskets, Geometric and group-theoretic approach. ELSEVIER Physica A () PHYSICA/ ' Representation of random walk in fractal space-time Ryutaro Kanno * National Institute Jor Fusion Science, , Oroshi-cho, Toki , Japan Received 16 August Abstract To analyze the anomalous diffusion on a fractal structure with fractal in the time axis, we propose a statistical representation given by a path integral method in Cited by:

Abstract: We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal Cited by: Along grain boundaries of quartz from metamorphic and igneous rocks complex interfingering (sutures) may occur. Under the light microscope the lengths of the sutures range from approximately 10– μm. The sutured grain boundaries are statistically self-similar over one to two orders of magnitude. They represent fractals. Their mathematical counterpart are Koch curves which Cited by:

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A Random Walk Through Fractal Dimensions Paperback – by Brian H. Kaye (Author) › Visit Amazon's Brian H. Kaye Page. Find all the books, read about the author, and more. See search results for this author. Are you an author. Learn about Author Central Cited by: of fractal geometry, an interest that led to the books “A Random Walk Through Fractal Dimensions” and “Chaos & Complexity.

Discovering the Surprising Patterns of Science and Technology”. The philosophical side of science has always interested him and has been complemented by his activities as a methodist local preacher in the Sudbury region.

A Random Walk Through Fractal Dimensions, Second Edition. Author(s): Professor Brian H. Kaye; This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin.

Get this from a library. A random walk through fractal dimensions. [Brian H Kaye] -- The aim of this book is both to stimulate interest in fractal geometry and to be useful as a first text to those who use fractal geometry in their work.

It contains many suggestions for experiments. A random walk through fractal dimensions. [Brian H Kaye] The aim of this book is both to stimulate interest in fractal geometry and to be useful as a first text to those who use fractal geometry in their work.

randomwalks on a rectangular lattice in two-dimensional space; the use of polar co-ordinates to describe random progress in two. Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite.

Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to. A Random Walk Through Fractal Dimensions, Second Edition Professor Brian H. Kaye(auth.) Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems.

The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. Brian H. Kaye is the author of A Random Walk Through Fractal Dimensions, 2nd Edition, published by Wiley.

More about Brian H. Kaye. A Random Walk Through Fractal Dimensions. A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.

An elementary example of a random walk is the random walk on the integer number line, which starts at 0 and at each step moves +1 or −1 with equal probability. A Random Walk Through Fractal Dimensions 2e is the English written work of Kaye.

The book is categorized in Physical Sciences & Engineering, Physics. Author: Kaye Book Name: A Random Walk Through Fractal Dimensions 2e eBook ISBN: Book Edition: 2nd Edition Main Category: Physical Sciences & Engineering Special Area: Physics UBCM: UBCM Special Product: [ ].

How to Calculate Fractal Dimension by Random walk method of 3-D surface. A Random Walk Through Fractal Dimensions. 2nd Edition. ByBrian H. Kaye. This paper computes the fractal dimensions of their process limits, which represent particle traces in anomalous diffusion.

Key words and phrases: Fractional Brownian motion, Lévy process, strictly stable process, continuous time random Cited by: Details. This Demonstration illustrates the random walk property where is the dispersion, is the number of steps, and is the size of a step.

The relation, a constant, is here shown to be the signature of a fractal dimension equal to The fractal dimension of an object is the power that links the number of smaller objects used to measure it and their typical length, which is called the.

of unaffected escape. Random walks through fractal sets with DF. Random walk on fractals: numerical studies in 20 1 number of sites in the gasket is given by N, = (d + 1)(1 + (d + 1)")/ scaling factor of the gasket is b=2 and the fractal dimensionality is (Gefen et a1 ) 6= In(d + l)/ln spectral dimensionality 2 was found in I: d'= 2 In(d + l)/ln(d + 3).

In the following, we shall study the RWS on the gasket at d = 2, in order to check some. A random walk through fractal dimensions. By Brian H Kaye. Abstract. Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite Author: Brian H Kaye.

A Random Walk Through Fractal Dimensions Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite.

This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions.

Signpost 6 Fractal Geometry and the Structure of Catalysts. Signpost 7 Solid‐state Physics. Signpost 8 Butterflies, Ants and Caterpillars in the Garden of Eden. Signpost 9 Turbulence and Chaos. Signpost 10 The Philosophical Impact of Fractal Geometry. Signpost 11 Fun with Fractal Logic.

Starting in the 17th century with notions of recursion, fractals have moved through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century by the seminal work of Bernard Bolzano, Bernhard Riemann, and Karl Weierstrass, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning.

Ziff RM, Cummings PT, Stell G () Generation of percolation cluster perimeters by a random walk. J Phys A ; Bunde A, Gouyet JF () On scaling relations in growth models for percolation clusters and diffusion fronts. J Phys A L; Weinrib A, Trugman S () A new kinetic walk and percolation perimeters.A Random Walk Through Fractal Dimensions 作者: Brian H.

Kaye 出版社: Wiley-VCH 出版年: 定价: USD 装帧: Paperback ISBN: 豆瓣评分. Output: Higher dimensions In higher dimensions, the set of randomly walked points has interesting geometric properties.

In fact, one gets a discrete fractal, that is, a set which exhibits stochastic self-similarity on large scales. On small scales, one can observe “jaggedness” resulting from the grid on which the walk is performed/5.