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Preface	p. vii
Growth and Form	p. 1
Paradigms of Pattern Formation: Towards a Computational Theory of Morphogenesis	p. 3
Introduction	p. 3
Single blind agent with finite memory	p. 6
Single blind agent with infinite memory	p. 7
Single sighted agent receiving cues from the environment (one-way exogenous control)	p. 8
Single sighted agent receiving cues from the structure (two-way exogenous control)	p. 10
Single self-controlled agent (endogenous control)	p. 11
Multiple blind agents with finite memory	p. 12
Multiple blind agents with infinite memory	p. 14
Multiple sighted agents	p. 14
Multiple endogenously-controlled agents	p. 16
Combined effect of multiple mechanisms	p. 18
Conclusions	p. 19
Growth and Form of Sponges and Corals in a Moving Fluid	p. 24
Introduction	p. 24
Biological background	p. 24
Simulation of growth in a mono directional flow	p. 26
Simulation of growth in a bidirectional (alternating) flow	p. 28
Methods	p. 29
Modelling the nutrient distribution	p. 29
Modelling the growth process in an alternating flow	p. 31
Results	p. 32
Discussion	p. 37
From Pseudo-Random Numbers to Stochastic Growth Models and Texture Images	p. 42
Introduction	p. 42
Pseudo-random number generators	p. 43
Growth models	p. 45
Eden's type growth models	p. 45
Conway's "Game of Life" and its modifications	p. 48
Algorithmic models of texture images	p. 54
The algorithmic approach to synthesis and analysis of texture images	p. 55
Crystal Growth, Biological Cell Growth, and Geometry	p. 65
Introduction	p. 65
A growing tree trunk whose shape oscillates wildly in time	p. 66
Cell growth versus crystal growth	p. 66
The groundrules	p. 66
The plan	p. 67
The coordination problem	p. 68
The signal problem	p. 68
The delay problem	p. 69
The signal cascade	p. 70
Using boundaries	p. 70
Measuring shape	p. 70
The example	p. 71
The geometry of rat tissue	p. 72
Discrete geometry	p. 72
Euclidean geometry, the lens of the eye, and muscle fibers	p. 73
Spherical geometry and the bladder	p. 73
Negatively curved geometry and the lung, brain, digestive, and endocrine systems	p. 73
Conflicting geometries	p. 74
Crystals	p. 75
Examples of crystals	p. 75
Ways of viewing crystals	p. 76
Negatively curved crystals are asymptotically fractal	p. 78
The Cayley crystal	p. 78
Thin triangles	p. 79
Asymptotic shape	p. 79
Fractal Theorem	p. 80
Proof	p. 80
Recent Results on Aperiodic Wang Tilings	p. 83
Introduction	p. 83
Algebraic construction of aperiodic tile sets	p. 87
Forced tiles and determinism	p. 89
Beyond aperiodicity	p. 93
Conclusions and open problems	p. 94
Reaction-Diffusion and Beyond	p. 97
Biological Pattern Formation as a Complex Dynamic Phenomenon	p. 99
The problem of pattern formation	p. 99
The egg cannot contain the final pattern	p. 100
Organizing regions	p. 100
The concept of positional information	p. 101
Generation of a primary pattern by autocatalysis and lateral inhibition	p. 101
The Activator-Inhibitor concept	p. 102
Comparison with Turing's mechanism	p. 105
The wave length problem--stabilization of a monotonic gradient by a feedback on the source density	p. 106
How to generate structures close to each other, how at a distance: head, foot and tentacle formation in Hydra	p. 108
Activation of genes under the influence of morphogenetic signalling	p. 110
Formation of filament-like branching structures	p. 113
Segmentation by mutual activation of cell states that locally exclude each other	p. 115
Pattern formation in secondary embryonic fields: differentiation borders obtain organizing properties	p. 116
Pigmentation pattern of shells of mollusk--a natural picture book to study dynamic systems	p. 117
Traces of a stable pattern, oscillations and travelling waves: lines parallel, perpendicular or oblique to the direction of growth	p. 118
Travelling waves with unusual properties	p. 119
Formation of branches: the sudden formation of backwards-running waves	p. 119
Penetration of waves without annihilation	p. 121
Not all together now	p. 123
Travelling waves without pace-maker	p. 124
Complex patterns result from the superposition of two patterns	p. 124
Superposition of two time-dependent patterns	p. 126
Open problems in shell patterning	p. 127
Andronov Bifurcations and Sea Shell Patterns	p. 133
Andronov bifurcations in extended systems	p. 136
Sea shell patterns	p. 139
Cavitation like patterns	p. 141
Patterns of excitable waves	p. 141
Rational and Irrational Angles in Phyllotaxis	p. 145
Introduction	p. 145
The geometry of phyllotaxis	p. 145
The dynamics of phyllotaxis	p. 146
The self organisation in model iterative systems	p. 147
Hofmeister's rules: the spiral modes	p. 147
The dynamical selection of the Fibonacci modes	p. 148
The generalised model: Snow and Snow's rules	p. 153
The selection of the actually observed patterns	p. 155
The selection during the plant growth	p. 156
Conclusions	p. 156
Cellular Patterns	p. 161
Organogenetic Cellular Patterning in Plants	p. 163
Introduction	p. 163
Cell patterning from the perspective of the cell body	p. 164
What lies behind analyses of cell patterning?	p. 167
A simple autoregenerating cell pattern related to organogenesis	p. 169
Simulation of cell patterns and the uncovery of division rules	p. 172
The Simulation System for the Psilotum Apex	p. 172
Identification of cell types	p. 177
Merophyte formation by apical divisions	p. 178
Wall-offsetting leads to refinement of the wall production system	p. 179
The distribution of apical triangular cells and the problem of dichotomous axis branching	p. 181
Possible regulatory factors underlying cell patterning and its simulation at the psilotum apex	p. 182
A System's View of Division Wall Site Selection	p. 182
Cytological View of Division Wall Site Selection	p. 186
Was there a precursor of the psilotum pattern?	p. 189
Prospects	p. 193
A Classification of Plant Meristems based on Cellworks (3D L-systems). The Maintainance and Complexity of Their Cellular Patterns	p. 199
Introduction	p. 199
Cellworks	p. 201
A classification of plant forms	p. 203
Specification of a cellwork system with double labelled walls	p. 208
How to find a Cellwork system with an autoreproductive initial cell	p. 209
Extended classification of plant forms	p. 210
Passage from one generating system to another	p. 212
Limits of the classification tables	p. 212
From topology to geometry	p. 212
Conclusion	p. 214
Plant Meristems and Their Patterns	p. 217
Introduction	p. 217
Patterns of the shoot apical meristem	p. 218
Developmental variation of cellular patterns	p. 218
The geometry of a growing apex	p. 222
Phyllotaxis	p. 224
Cellular patterns of vascular cambium	p. 228
Storied pattern	p. 229
The pattern of growth activity	p. 231
Structural wavy patterns	p. 232
Conclusions	p. 235
Mechanical Stress Patterns in Plant Cell Walls and Their Morphogenetical Importance	p. 240
Introduction	p. 240
Stress anisotropy	p. 240
Stress distribution	p. 245
Conclusions	p. 248
Tensorial Model for Growth and Cell Division in the Shoot Apex	p. 252
Symplastic Growth and the Growth Tensor	p. 252
Model for Growth and Cell Division in the Shoot Apex (2-dimensional)	p. 254
The Example of Application of the Model	p. 259
Discussion	p. 263
DNA and Genetic Control	p. 269
DNA Nanotechnology: From Topological Control to Structural Control	p. 271
DNA Nanotechnology	p. 271
Double Helical DNA	p. 272
Genetic Recombination and the Holliday Junction	p. 274
Immobile Branched Junctions	p. 275
Characterization of Unusual DNA Motifs and Structures	p. 277
DNA Ligation and Cohesion	p. 278
Branched DNA and Sticky Ends	p. 280
Connectivity	p. 281
Topological Features of DNA Constructs	p. 281
Construction of DNA Polyhedra	p. 282
DNA Catenanes and Knots	p. 286
Construction of DNA Knots	p. 288
DNA Borromean Rings	p. 289
Rigid Components	p. 292
1-D and 2-D Periodic Arrays	p. 294
Nanomechanical Devices	p. 297
Prospects	p. 300
3D DNA Patterns and Computation	p. 310
Introduction	p. 310
Constructing Graphs with k-Armed Branched Molecules	p. 312
The Hamiltonian cycle problem	p. 312
The Three Vertex Colorability Problem (3VC)	p. 315
Recognition of Graph Structures	p. 318
Covering graphs and complexity	p. 318
Graphs made of one single stranded DNA molecule	p. 319
Final Remarks	p. 321
Circular Suggestions for DNA Computing	p. 325
Introduction	p. 325
Naturally Occurring Plasmids	p. 326
The Delphic Plasmid, DEL	p. 327
Independent Subsets and Vertex Covers for Undirected Graphs	p. 329
Partitions into Hamiltonian Subgraphs	p. 331
Satisfiability of Boolean Formulas	p. 332
DNA Computing by Matching: Sticker Systems and Watson-Crick Automata	p. 336
Introduction	p. 336
DNA: Structure and Annealing Operation	p. 339
Formal Language Theory Prerequisites	p. 341
The Twin-shuffle Language and its Relation with DNA	p. 342
The Operation of Sticking	p. 344
Sticker Systems	p. 346
The Power of Sticker Systems	p. 349
Watson-Crick Finite Automata	p. 352
The Power of Watson-Crick Finite Automata	p. 353
Variants of Watson-Crick Automata	p. 356
Conclusions	p. 359
Images and Perception	p. 363
Aspects of Human Shape Perception	p. 365
Shape from motion	p. 365
From moving to static shapes	p. 367
Static shapes: the gestalt approach	p. 367
Static shapes: the importance of orientations	p. 370
2D perceptual geometry	p. 373
From 2D to 3D	p. 374
Shape synthesis	p. 378
Pattern Recognition in The Visual System and The Nature of Neural Coding	p. 382
Introduction	p. 382
The efficiency of pattern recognition by the human visual system	p. 382
The Coding Problem	p. 385
An alternative--Using patterns of spikes	p. 386
Rank Order Coding	p. 387
Rank Order Decoding	p. 388
Conclusions and Perspectives	p. 390
How can Singularity Theory Help in Image Processing?	p. 392
Introduction	p. 392
Digital images	p. 395
Compression problem	p. 396
An example of data representation, based on normal forms of singularities	p. 400
Singularities of digital images and their normal forms	p. 402
Detection of singularities and their approximation by normal forms	p. 408
Vectorized images	p. 415
Creation of virtual worlds	p. 418
Possible implications for human visual perception	p. 423
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Pattern Formation in Biology, Vision and Dynamics

9810237928

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