IN PLANTS

1998, LII + 836 pages
World Scientific,
Singapore, New Jersey, London, Hong Kong
ISBN 981 02 2621 7

It is volume 4 in WS Series in Mathematical Biology and Medicine
(P. M. Auger and R. V. Jean, Series Editors).
A collective book (44 authors from 14 countries).
Edited by Roger V Jean (Univ. Québec, Rimouski, Canada)
& Denis Barabé (U. Montréal, Inst. Recherche Biol. Veg, Montreal Botanical Garden).


The book deals with biological, mathematical, descriptive, causal and systemic phyllotaxis. It aims at reflecting the widest possible range of ideas and researches closely related to phyllotaxis and contains 30 well illustrated chapters, four prologues and a foreword.

The book has three parts of equal importance. The first two parts concern data collecting, pattern recognition and pattern generation to which students of phyllotaxis are well accustomed. The third part is devoted to the problem of origins of phyllotactic patterns, giving the field of phyllotaxis the universality it requires to be fully understood.

Phyllotaxis-like patterns are found in places where genes are not necessarily present. Part III concerns general comparative morphology, homologies with phyllotactic patterns, and recent trends on evolution that can help to understand phyllotaxis.

The distinguished researchers who accepted to participate in the production of this book, strongly contributed to the field of phyllotaxis in the past and have devoted a lot of their time to the fascinating subject coming up with most valuable findings, or are newcomers with original ideas that may be very relevant for the future of the field. The book summarizes and updates their contributions, and promotes new avenues in the treatment of phyllotaxis.

This book on mathematical and biological phyllotaxis is the first collective book ever. A landmark in the history of phyllotaxis.


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R. V. Jean (Univ. of Québec, Rimouski) and D. Barabé(Inst. Rech. Biol. Vég., Canada)
Prologue by a Mathematicien: The Role of mathematics in phyllotaxis xiii
I. Adler (North Bennington, Vermont)
Prologue by a Botanist: Phyllotactic Symmetry in Plant Growth xvii
R. O. Erickson (U. of Pennsylvania, USA)
Prologue by a Molecular Geneticist: The Role of Homeotic Genes and of Molecular Mimicry in the Determination of Plant and Animal Symmetries xxvii
A. Lima-de-Faria (University of Lund, Sweden)
Prologue by a Crystallographer: Phyllotaxis xxxv
A. L. Mackay (University of London, U. K.)
List and addresses of Contributors
Table of Contents

1. Investigation of Phyllotaxis of Rhododendron 3
L.A. Bursill and J. L. Rouse (U. of Melbourne, Australia)
2. Systems of Phyllotaxis in the Genus Eucalyptus in relation to Shoot Architecture 33
D. J. Carr (Australian National University)
3. Pendulum Symmetry 61
W. A. Charlton (University of Manchester, England)
4. Phyllotaxis in the Vitaceae 89
J. M. Gerrath (University of Northern Iowa, USA)
C. R. Lacroix (Univ. of Prince Edward Island)
U. Posluszny (University of Guelph, Canada)
5. Phyllotaxis in Flowers and in Flower Reversion 109
R. F. Lyndon (University of Edinburgh, Scotland)
6. Decussate to Spiral Transitions in Phyllotaxis 125
R. D. Meicenheimer (Miami University, Oxford)
7. The Physiological Basis of Pattern Generation in the Sunflower 145
J. H. Palmer (Univ. of New South Wales, Australia)
8. Plastochrone Ratio and Leaf Arc as Parameters of a Quantitative Phyllotaxis Analysis in Vascular Plants 171
R. Rutishauser (University of Zurich, Switzerland)
9. Changes in Phyllotactic Pattern Structure in Pinus L. due to Changes in Altitude 213
I. I. Vakarelov (Univ. of Forestry, Bulgaria)
10. Biastrepsis and Allomery of stems of Dipsacus Sylvestris 231
J. Vieth (Inst. recherche en biol. vegétale, U. Montréal)

11. Generating Phyllotaxis Patterns on a Cylindrical Point Lattice 249
I. Adler (North Bennington, Vermont)
12. Modeling Meristic Characters of Asteracean Flowerheads 281
J. Battjes (Institut für Pflanzengenetick, The Netherlands)
P. Prusinkiewicz (University of Calgary, Canada)
13. The Shape of Dirichlet Regions in a Coxeter Lattice as a function of Divergence and Rise 313
R. Dixon (Mathographics, London, U.K.)
14. The Selection of Phyllotactic Patterns 335
S. Douady (École Normale Supérieure, Paris)
15. How Plants Produce Pattern. A Review and a Proposal that undulating Field is the Mechanism 359
P. B. Green,
C. R. Steele and
S. C. Rennich (Stanford University, Stanford)
16. The Crocograph and its Practical Utility in Phyllotaxis 393
N. Hallé (Cherbourg, France)
17. Phyllotaxis as a Dynamical System: A Study in Number 409
J. Kappraff,
D. Blackmore and
G. Adamson (New Jersey Institute of Technology)
18. Phyllotaxis as a Geometrical and Dynamical System 459
A.-J. Koch,
G. Bernasconi and
F. Rothen (Université de Lausanne, Suisse)
19. Creating Phyllotaxis from Seed to Flower 487
F. M. J. van der Linden (U. of Eindhoven, Netherlands)
20. The Role and Importance of Vertical Spacing at the Plant Apex in determining Phyllotactic Pattern 523
W. W. Schwabe (University of London, England)

21. The Phyllotactic Patterns as Resulting from Self- Organization in an Iterative Process 539
S. Douady and Y. Couder (École Normale Supérieure, Paris)
22. Universal results from a Simple Model of Phyllotaxis 571
J. Guerreiro and F. Rothen (Université de Lausanne)
23. Elementary Rules of Growth in Phyllotaxis 601
R. V. Jean (Université du Québec, Rimouski)
24. Universality in Phyllotaxis: A mechanical Theory 619
H. Lee and
L. S. levitov (Massachusett Institut of Technology)
25. The Atomic Origin of Structural Periodicity 655
A. Lima-de-Faria (University of Lund, Sweden)
26. Uniform Spacing Models for the Morphogenesis of High Symmetry Biological Structures: Icosahedral Capsids, Coaxial Helices, and Helical Phyllotaxis. 681
C. J. Marzec (State University of New York, Albany)
27. Models of Pattern Formation Applied to Plant Development 723
H. Meinhardt (Max-Planck Institute, Germany),
A.-J. Koch and
G. Bernasconi (Université de Lausanne)
28. Light Harvesting 'Fitness Landscapes' for vertical Shoots with Different Phyllotactic Patterns 759
K. J. Niklas (Cornell University, USA)
29. On the Origin of Symmetry, Branching and Phyllotaxis in Land Plants 775
R. Sattler (McGill University, Montreal)
30. Quasicrystalline Pattern Formation in Fluids Substrates and Phyllotaxis 795
A. M. Selvam (Indian Institute of Tropical Meteorology India)

Subject Index
Authors Index