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From the stripes of a zebra and the spots on a leopard's back to the ripples on a sandy beach or desert dune, regular patterns arise everywhere in nature. The appearance and evolution of these phenomena have been a focus of recent research activity across several disciplines. This book provides an introduction to the range of mathematical theory and methods used to analyze and explain these often intricate and beautiful patterns. Bringing together several different approaches, from group theoretic methods to envelope equations and theory of patterns in large-aspect ratio-systems, the book also provides insight behind the selection of one pattern over another.Read more
- Accessible description of the mathematical theory behind fascinating pattern formation in areas such as biology, physics and materials science
- Collects recent research for the first time in an upper level textbook
- Features a number of exercises - with solutions online - and worked examples
Reviews & endorsements
"Rebecca Hoyle's book is an invaluable graduate text for those who first enter the field of Pattern Formation. It has a remarkably lucid style and friendly exposition and very balanced level of detail through the book. An important strength is its rigorous mathematical approach which equips the reader with the underlying understanding of the mechanisms of pattern formation and enables one to confidently investigate novel problems...I find it remarkable that a book presenting a field that has recently grown to such proportions, feels so light and approachable when you first take it in your hands. This is, I think, a much needed encouragement for the beginner. The uncluttered chapter structure and also the nice publisher design play a role in this."
UK Nonlinear NewsSee more reviews
"Altogether, Hoyle has in her book created a rich and inviting exposition (including, for example, many illustrative pictures), suitable either as a reference source or as a course book for graduate students or perhaps even advanced undergraduates."
"...I have recommended this book to all my graduate students. It provides a useful starting point for those of us interested in the theory of pattern formation and is well suited as a text for a first course on pattern formation."
Edgar Knobloch, Physics Today
"... An engaging foray into understanding the mathematics of patterns and serves as a good source for active researchers in the field."
Tom Schulte, Oakland University for MAA Reviews
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- Date Published: April 2006
- format: Hardback
- isbn: 9780521817509
- length: 434 pages
- dimensions: 257 x 211 x 30 mm
- weight: 1.11kg
- contains: 130 b/w illus. 20 colour illus. 9 tables 50 exercises
- availability: Available
Table of Contents
1. What are natural patterns?
2. A bit of bifurcation theory?
3. A bit of group theory?
4. Bifurcations with symmetry
5. Simple lattice patterns
6. Superlattices, hidden symmetries and other complications
7. Spatial modulation and envelope equations
8. Instabilities of stripes and travelling plane waves
9. More instabilities of patterns
10. Spirals, defects and spiral defect chaos
11. Large-aspect-ratio systems and the Cross-Newell equations.
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