# Book:Brian H. Kaye/A Random Walk through Fractal Dimensions

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## Brian H. Kaye:

## Brian H. Kaye: *A Random Walk through Fractal Dimensions*

Published $\text {1989}$, **VCH Publishers**

- ISBN 0-89573-888-0.

### Subject Matter

### Contents

- Preface (Sudbury, January 1989)
- Acknowledgments

- Word Finder
- Coloured Plates

**1 A Starting Point for the Randomwalk**- References

**2 Fractal Description of Fineparticle Boundaries**- 2.1 The Fractal Dimensions of a Famous Carbonblack Profile
- 2.2 The Dangerous Art of Extrapolation for Predicting Physical Phenomena
- 2.3 Discovering Texture Fractals
- 2.4 Experimental Methods for Characterising Fineparticle Boundaries

- References

**3 What Use are Fractals?**- 3.1 Elegance and Utility of Fractal Dimensions
- 3.2 Fractal Description of Powder Metal Grains and Special Metal Crystals
- 3.3 Fractals and the Flow of Dry Powders
- 3.4 Fractals in the Mining Industry
- 3.5 Fractal Structure of Cosmic Fineparticles
- 3.6 Fractal Structure of Some Types of Sand Grains
- 3.7 Fractal Structure of Some Respirable Dusts
- 3.7.1 What is the Technical Meaning of Respirable Dust?
- 3.7.2 Is Fumed Silica a Respirable Hazard?
- 3.7.3 Dust from Nuclear Reactor Systems
- 3.7.4 Fuse Fumes and Welding Dust
- 3.7.5 Characteristics of Dust Generated by Explosions
- 3.7.6 Diesel Soot and Fumed Pigments
- 3.7.7 Fractal Specimens of Flyash

- 3.8 Polymer Grains and Rubber Crumbs
- 3.9 Fineparticle Look-Alike:

- References

**4. Delinquent Coins and Staggering Drunks**- 4.1 A Capricious Selection of Terms that Describe Random Events
- 4.2 Chance, Probability and Error
- 4.3 Monte Carlo Technique for Studying Stochastic Processes
- 4.4 Randomwalks in One-Dimensional Space
- 4.5 Delinquent Coins and Cantorian Dusts
- 4.6 The Devil's Staircase and Crystal Structure
- 4.7 Pin-ball Machines and Some Random Thoughts on the Philosophical Significance of Fractal Dimensions
- 4.8 Plumes with Fractal Boundaries
- 4.9 Gaussian Graph Paper, Fractal Distributions and Elephants in the Face Powder

- References

**5 Fractal Systems Generated by Randomwalks in Two-Dimensional Space**- 5.1 Randomwalks on a Rectangular Lattice in Two-Dimensional Space
- 5.2 The Use of Polar Cc-ordinates to Describe Random Progress in Two-Dimensional Space
- 5.3 Randomwalk Modelling of Fractal Deposits in Two-Dimensional Space
- 5.4 Pigmented Coatings and Percolating Systems
- 5.5 Mathematical Description of Fractal Clusters
- 5.6 Percolating Pathways and Scaling Properties
- 5.7 The Fractal Structure of Clusters Generated by Diffusion-Limited Aggregation (DLA)

- References

**6 Vanishing Carpets, Fractal Felts and Dendritic Capture Trees**- 6.1 Sierpinski Carpets and Swiss Cheese
- 6.2 A Fractal Description of the Deposition Efficiency of Simulated Pesticide Spray Systems
- 6.3 Sierpinski Fractal Description of Real Dispersed Systems
- 6.4 Exploring the Fractal Structures of Filters
- 6.5 Dendritic Capture Trees in Filter Systems
- 6.6 Cantor on the Rocks

- References

**7 An Exploration of the Physical Significance of Fractal Structures in Three-Dimensional Space**- 7.1 Randomwalk Theory of Powder Mixing in Three- and Four-Dimensional Space
- 7.2 Fractal Geometry and Aerosol Physics
- 7.3 Assessing the Fractal Structure of a Rough Surface from Adsorption Studies
- 7.4 Interpreting Intrusion Porosimetry Data from a Fractal Geometry Perspective

- References

**8 Fractal Fingers and Floods**- 8.1 Fractal Fingers
- 8.2 Fractal Floods and Fronts in Porous Media

- References

**9 Fracture, Fragments and Fractals**- 9.1 The Fractal Structure of Fractured Surfaces
- 9.2 Describing Progress of a Fracture Process From a Fractal Perspective
- 9.3 The Fragmentation Fractal. A New Fractal Dimension for Characterising a Fragmented System
- 9.4 Fractal Geometry and New Perspectives in the Mineral Processing Industry
- 9.4.1 Dust Explosions
- 9.4.2 Energy Efficiency in a Pulverization Process

- 9.5 Brainstorming About Fractal Geometry and the Fracture Resistance of Composite Materials

- References

**10 Signposts to More Rambling Explorations of Fractal Space**- Signpost 1 General Ramblings
- References
- Signpost 2 Fractal Scenery and Artistic Vision
- References
- Signpost 4 Lakes, Islands and other Geofractals
- References
- Signpost 5 Trees, Crabs, Cauliflowers and Camouflage
- References
- Signpost 6 Fractal Geometry and the Structure of Catalysts
- References
- Signpost 7 Solid-state Physics
- References
- Signpost 8 Butterflies, Ants and Caterpillars in the Garden of Eden
- References
- Signpost 9 Turbulence and Chaos
- References
- Signpost 10 The Philosophical Impact of Fractal Geometry
- Signpost 11 Fun with Fractal Logic
- References

- Author Index
- Subject Index