Phyllotaxis: a systemic study in plant morphogenesis
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| Main Author: | |
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| Format: | Book |
| Language: | Undetermined |
| Published: |
Cambridge u.a.
Cambridge Univ. Press
1994
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 386 S. graph. Darst. |
| ISBN: | 0521404827 |
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| 245 | 1 | 0 | |a Phyllotaxis |b a systemic study in plant morphogenesis |c Roger V. Jean |
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Record in the Search Index
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| adam_text | Contents
Acknowledgments page xiv
Prologue 1
1. Subject and aims of the book 1
2. The problem of origins of phyllotactic patterns 3
3. The level of presentation 4
4. Related works in the field 5
Part I Pattern recognition
Introduction 9
1. The centric representation 11
1.1. Parastichy pairs (m, n) 11
1.1.1. Patterns in plants 11
1.1.2. Whorled and spiral patterns 12
1.1.3. Contact parastichies 13
1.2. Basic concepts 16
1.2.1. Visible opposed parastichy pairs 16
1.2.2. Genetic spiral and the Bravais Bravais
theorem 19
1.2.3. Divergence angle d and plastochrone ratio R 20
1.3. Mathematical constants 20
1.3.1. Fibonacci and Lucas sequences 20
1.3.2. The golden ratio t 22
1.3.3. Relationships between the constants 23
1.4. A model for pattern analysis 24
1.4.1. Geometry of the spiral lattice 24
1.4.2. A mathematical puzzle 26
1.5. Problems 28
2. The fundamental theorem and its applications 31
2.1. A cornerstone in phyllotaxis insight into history 31
vii
viii Contents
2.2. Introduction to the theorem 33
2.2.1. Visible opposed parastichy pairs for the
Fibonacci angle 33
2.2.2. Phyllotactic fractions associated with the
Fibonacci angle 35
2.3. The fundamental theorem of phyllotaxis 36
2.3.1. Various forms 36
2.3.2. Useful algorithms relating d and (m, n) 38
2.4. Interpretation of spiromonostichy in Costus and
Tapeinochilus 41
2.5. Bravais Bravais approximation formula 43
2.5.1. The cylindrical lattice 43
2.5.2. Derivation of the formula 45
2.6. Problems 46
3. Hierarchical control in phyllotaxis 48
3.1. Lestiboudois Bolle theory of duplications 48
3.2. Zimmermann telome theory 52
3.2.1. Ancestral land plants 52
3.2.2. Algal ancestors 53
3.2.3. Vascular phyllotaxis 57
3.3. Translocation of substances in plants 59
3.4. Hierarchies arising from modeling 61
3.4.1. Van der Linden model 61
3.4.2. The fractal nature of phyllotaxis 63
3.5. The hierarchical representation of phyllotaxis 67
3.5.1. Hierarchies with only simple and double nodes 67
3.5.2. Growth matrices, L systems, and Fibonacci
hierarchies 69
3.6. Problems 73
4. Allometry type model in phyllotaxis 76
4.1. Differential growth in the plant apex 76
4.2. The model 77
4.2.1. Derivation of the model 77
4.2.2. Interpretation of the model 80
4.3. Generalized Coxeter formula 82
4.4. Derivation of the Richards phyllotaxis index 83
4.5. The Pattern Determination Table 85
4.6. Apical size and phyllotaxis of a system 87
4.6.1. Church bulk ratio 87
4.6.2. Richards area ratio 90
4.6.3. The plastochrone P 92
4.7. Problems 93
Contents ix
5. Practical pattern recognition 96
5.1. The necessity of theoretical frameworks 96
5.2. Applications of the allometry type model 98
5.2.1. Linear relations in an expanding apex 98
5.2.2. Phyllotaxis in Silene, a function of temperature 100
5.3. On the theoretical determination of the plastochrone
ratio 101
5.3.1. Various models to use 101
5.3.2. Advantages of the allometry type model 102
5.4. Assessing phyllotactic patterns 104
5.4.1. Maksymowych Erickson method using Xanthium 104
5.4.2. A first method using the Pattern Determination
Table 105
5.4.3. Evaluating the phyllotactic patterns for
Proserpinaca and Xanthium 106
5.5. Other applications of the Pattern Determination Table 108
5.5.1. The practical limits of the Richards phyllotaxis
index 108
5.5.2. A second method using the Pattern
Determination Table 108
5.5.3. Evaluating phyllotactic patterns in
Chrysanthemum and Linum 109
5.6. Difficulties involved in pattern recognition 111
5.6.1. Data collection and Fujita s normal curves 111
5.6.2. Interpretation of particular lattices 113
5.6.3. Interpretation of phyllotactic fractions 116
Epilogue 120
Part II Pattern generation: a key to the puzzles
Introduction 123
6. An interpretative model 127
6.1. The necessity of denning entropy measures 127
6.1.1. An a disciplinary concept 127
6.1.2. Entropy in phyllotaxis 128
6.2. Dynamic versus static approaches 131
6.2.1. Principle of minimal entropy production 131
6.2.2. Particular notions of rhythm 133
6.3. The optimal designs 135
6.4. Results and predictions of the model 138
6.4.1. Patterns that can and cannot exist 138
6.4.2. Multijugate systems 141
6.5. By products and applications 142
x Contents
1. Testing the interpretative model 145
7.1. Searching for quantified observations 145
7.2. Data on the frequencies of occurrence of patterns 147
7.3. About aberrant spiral patterns 152
7.3.1. List of problematic patterns 152
7.3.2. On the sequence 2 6,13,19,32, ... 152
7.3.3. On the sequence 3,14,17,31,48,...) 153
7.3.4. On the sequence 3,8,11,19,30, ... 153
7.3.5. On the sequence 3,7,10,17,27, ... 154
7.4. Conclusions and discussion 155
7.4.1. Compilation of the data 155
7.4.2. On the frequency of the pattern 1,2,3,5,8,...) 155
7.4.3. Relative frequency of occurrence of the
sequences 1,3,4,7,11,...) and 2 1,2,3,5,8, ... 157
7.4.4. Insufficiency of the data available 158
7.4.5. Remarks on methodology 158
8. The interpretative model and whorled patterns 160
8.1. Multimerous patterns 160
8.2. Preliminary relationships among the patterns 161
8.2.1. Multimery versus multijugy 161
8.2.2. Schoute s false whorls 162
8.3. Transitions between patterns 163
8.3.1. Continuous and discontinuous transitions
natural and induced 163
8.3.2. The mechanism of transition 165
8.4. The primitiveness of spirality 166
8.4.1. Evolutionary levels in pattern generation 166
8.4.2. Methodological consequences on modeling 168
8.5. Fundamental relationships among the patterns 169
8.5.1. Generating alternating multimery from
multijugate normal systems with / = 2
the first hypothesis 169
8.5.2. Alternating multimery derivation from
anomalous systems the second hypothesis 171
8.5.3. Superposed whorls are normal multijugate
systems 172
8.5.4. Summary of the model and existence of
predicted patterns 172
8.6. Predictive and explanatory values of the interpretative
model 176
8.6.1. Analysis of the phyllotaxis of Dipsacus 176
8.6.2. Correlation with other models 179
8.6.3. Perturbed patterns 181
Contents xi
9. Convergences among models 185
9.1. Basic morphology of phyllotactic patterns 185
9.1.1. Packing efficiency; the noble numbers 185
9.1.2. Self similarity 188
9.2. Derivation of the r model 192
9.2.1. Distances on the phyllotactic allometric line 192
9.2.2. Minimality principles 192
9.3. Ordering the noble numbers 193
9.4. The 7 model and the interpretative model 195
9.5. Marzec entropy and diffusion model 196
9.5.1. Phyllotaxis as a dissipative structure 196
9.5.2. Relationships between the two entropy
models of phyllotaxis 198
9.5.3. Priority order in phyllotactic systems 198
9.6. Adler contact pressure model 199
9.6.1. The maximin principle and its consequences 199
9.6.2. Comparison with the minimality condition of
the r model 201
9.7. Fujita s a priori spiral patterns 202
Epilogue 204
Part III Origins of phyllotactic patterns
Introduction 207
10. Exotic phyllotaxis 209
10.1. Historical meeting again 209
10.2. Phyllotaxislike patterns 211
10.2.1. In biology 211
10.2.2. In cylindrical crystals 212
10.3. Structure of polypeptide chains 214
10.3.1. Protein crystallography and systems research 214
10.3.2. Mathematical analysis of protein lattices and
predictions 219
10.4. Generalized crystallography 222
10.4.1. The unit cell of a crystal 222
10.4.2. Multimery, multijugy, and transitions
revisited 222
10.4.3. The daisy: a living crystal 226
10.4.4. Minimal energy costs with regular
transitions 227
11. Morphogenetical parallelism and autoevolutionism 229
11.1. General comparative morphology 229
11.2. Isomorphisms with phyllotactic patterns 231
11.2.1. Minerals, animals, and artifacts 231
xii Contents
11.2.2. Colloidal crystals, quasicrystals, and
polymers 233
11.2.3. Properties of space time 236
11.3. Isofunctionalism with phyllotaxis 238
11.3.1. Branching processes 238
11.3.2. Gnomonic growth 239
11.4. Levels of organization and layers of models 243
11.5. A universal framework for the study of phyllotaxis 246
11.5.1. Tenets of autoevolutionism 246
11.5.2. Autoevolutionism and neo Darwinism 247
12. The challenge redefined 250
12.1. Early hypotheses 250
12.1.1. General dissatisfaction with chemical
hypotheses 250
12.1.2. General dissatisfaction with physical
hypotheses 252
12.2. Well grounded models 255
12.2.1. Light and water 255
12.2.2. Lines of force and energy 257
12.3. Synergy and systems research 259
12.3.1. A pyramid of models 259
12.3.2. Biological and mathematical phyllotaxis 260
12.3.3. Systemic phyllotaxis 261
12.3.4. Phyllotaxis, magnetic fields, and
superconductors 262
12.4. The whole is in the part 265
12.4.1. Spirality and branching everywhere 265
12.4.2. Prebiotic and modern creations 266
12.4.3. A multidisciplinary problem 267
Epilogue 270
Part IV Complements
Introduction 273
Appendixes 275
1. Glossary 275
2. Answers to problems 290
A2.1. Chapter 1 290
A2.2. Chapter 2 292
A2.3. Chapter 3 295
A2.4. Chapter 4 296
3. Questions 299
4. General properties of phyllotactic lattices 304
Contents xiii
A4.1. Phyllotaxis and Farey sequences 304
A4.2. Visible parastichy pairs 307
A4.3. Examples and algorithms 309
5. The Williams Brittain model 312
A5.1. The mechanism 312
A5.2. The results 314
6. Interpretation of Fujita s frequency diagrams in
phyllotaxis 317
7. L systems, Perron Frobenius theory, and the growth
of filamentous organisms 321
A7.1. Preliminaries 321
A7.2. Theorems and applications 323
8. The Meinhardt Gierer theory of pre pattern
formation 326
9. Hyperbolic transformations of the cylindrical lattice 329
Bibliography 333
Author index 372
Subject index 376
|
| any_adam_object | 1 |
| author | Jean, Roger V. |
| author_facet | Jean, Roger V. |
| author_role | aut |
| author_sort | Jean, Roger V. |
| author_variant | r v j rv rvj |
| building | Verbundindex |
| bvnumber | BV009562446 |
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| ctrlnum | (OCoLC)246544729 (DE-599)BVBBV009562446 |
| dewey-full | 581.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 581 - Specific topics in natural history of plants |
| dewey-raw | 581.4 |
| dewey-search | 581.4 |
| dewey-sort | 3581.4 |
| dewey-tens | 580 - Plants |
| discipline | Biologie |
| format | Book |
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| id | DE-604.BV009562446 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:37:11Z |
| institution | BVB |
| isbn | 0521404827 |
| language | Undetermined |
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| publisher | Cambridge Univ. Press |
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| spelling | Jean, Roger V. Verfasser aut Phyllotaxis a systemic study in plant morphogenesis Roger V. Jean Cambridge u.a. Cambridge Univ. Press 1994 XIV, 386 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Pflanzen (DE-588)4045539-7 gnd rswk-swf Musterbildung (DE-588)4137934-2 gnd rswk-swf Pflanzenmorphologie (DE-588)4045572-5 gnd rswk-swf Morphogenese (DE-588)4132460-2 gnd rswk-swf Pflanzen (DE-588)4045539-7 s Musterbildung (DE-588)4137934-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Morphogenese (DE-588)4132460-2 s Pflanzenmorphologie (DE-588)4045572-5 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006319111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jean, Roger V. Phyllotaxis a systemic study in plant morphogenesis Mathematisches Modell (DE-588)4114528-8 gnd Pflanzen (DE-588)4045539-7 gnd Musterbildung (DE-588)4137934-2 gnd Pflanzenmorphologie (DE-588)4045572-5 gnd Morphogenese (DE-588)4132460-2 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4045539-7 (DE-588)4137934-2 (DE-588)4045572-5 (DE-588)4132460-2 |
| title | Phyllotaxis a systemic study in plant morphogenesis |
| title_auth | Phyllotaxis a systemic study in plant morphogenesis |
| title_exact_search | Phyllotaxis a systemic study in plant morphogenesis |
| title_full | Phyllotaxis a systemic study in plant morphogenesis Roger V. Jean |
| title_fullStr | Phyllotaxis a systemic study in plant morphogenesis Roger V. Jean |
| title_full_unstemmed | Phyllotaxis a systemic study in plant morphogenesis Roger V. Jean |
| title_short | Phyllotaxis |
| title_sort | phyllotaxis a systemic study in plant morphogenesis |
| title_sub | a systemic study in plant morphogenesis |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Pflanzen (DE-588)4045539-7 gnd Musterbildung (DE-588)4137934-2 gnd Pflanzenmorphologie (DE-588)4045572-5 gnd Morphogenese (DE-588)4132460-2 gnd |
| topic_facet | Mathematisches Modell Pflanzen Musterbildung Pflanzenmorphologie Morphogenese |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006319111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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