Meinhardt The Algorithmic Beauty of Sea Shells

4. Auflage 2009
ISBN: 978-3-540-92142-4
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 269 Seiten

The pigment patterns on tropical shells are of great beauty and diversity. Their mixture of regularity and irregularity is fascinating. A particular pattern seems to follow particular rules but these rules allow variations. No two shells are identical. The motionless patterns appear to be static, and, indeed, they consist of calci?ed material. However, as will be shown in this book, the underlying mechanism that generates this beauty is eminently dynamic. It has much in common with other dynamic systems that generate patterns, such as a wind-sand system that forms large dunes, or rain and erosion that form complex rami?ed river systems. On other shells the underlying mechanism has much in common with waves such as those commonly observed in the spread of an epidemic. A mollusk can only enlarge its shell at the shell margin. In most cases, only at this margin are new elements of the pigmentation pattern added. Therefore, the shell pattern preserves the record of a process that took place over time in a narrow zone at the growing edge. A certain point on the shell represents a certain moment in its history. Like a time machine one can go into the past or the future just by turning the shell back and forth. Having this complete historical record opens the possibility of decoding the generic principles behind this beauty.

Autoren/Hrsg.

Meinhardt, Hans

Inhaltsverzeichnis

1;Preface;6
2;Contents;10
3;1 Shell patterns - a natural picture book to study dynamic systems and biological pattern formation;14
3.1;1.1 Dynamic systems everywhere;14
3.2;1.2 Pattern formation;15
3.3;1.3 Dynamic systems are difficult to predict;16
3.4;1.4 Pattern formation in biology;17
3.5;1.5 Most shell patterns preserve a faithful time record;18
3.6;1.6 Elementary patterns: Lines perpendicular, parallel and oblique to the direction of growth;19
3.7;1.7 Oblique lines;21
3.8;1.8 Relief-like patterns follow the same rules;22
3.9;1.9 Many open questions and some hints;23
3.10;1.10 The hard problem: complex patterns;28
3.11;1.11 Earlier attempts to understand shell patterns;30
4;2 Pattern formation by local self-enhancement and long range inhibition;32
4.1;2.1 The activator -- inhibitor scheme;32
4.2;2.2 Stable patterns require a rapid antagonistic reaction;33
4.3;2.3 Periodic patterns in space;34
4.4;2.4 The width of stripes and the role of saturation;38
4.5;2.5 Early fixation of a pattern;40
4.6;2.6 The activator - depleted substrate scheme;42
4.7;2.7 The influence of growth;43
4.8;2.8 Inhibition via destruction of the activator;45
4.9;2.9 Autocatalysis by an inhibition of an inhibition;46
4.10;2.10 Formation of graded concentration profiles;48
4.11;2.11 Pattern formation in two dimensions;51
5;3 Oscillations and traveling waves;54
5.1;3.1 The coupling between the oscillators by diffusion;57
5.2;3.2 The width of bands and interbands;60
5.3;3.3 Oblique lines: traveling waves in an excitable medium;60
5.4;3.4 Traveling waves require a pace-maker region;62
6;4 Superposition of stable and periodic patterns;66
6.1;4.1 The formation of undulating lines and the partial synchronization of cells by activator diffusion;67
6.2;4.2 Reducing wave termination with a longer activation period;71
6.3;4.3 Interconnecting wavy lines and the formation of arches;71
6.4;4.4 Hidden waves;73
6.5;4.5 Pattern on the shell of Nautilus pompilius;74
6.6;4.6 Stabilizing an otherwise oscillating pattern by diffusion;75
6.7;4.7 Combinations of oscillating and nonoscillating patterns;76
6.8;4.8 Rows of patches parallel to the direction of growth;76
6.9;4.9 The possible role of a central oscillator;79
6.10;4.10 Conclusion;81
7;5 Crossings, meshwork of oblique lines and staggered dots: the combined action of two antagonists;84
7.1;5.1 Displacement of stable maxima or enforced de-synchronization by a second antagonist;84
7.2;5.2 Pattern variability;86
7.3;5.3 Global pattern rearrangements;87
7.4;5.4 Traces of the additional inhibition: oblique lines initiated or terminated out of phase;89
7.5;5.5 Crossings and branching;92
7.6;l5.6 Changing the wave speed before and during collisions;95
7.7;5.7 Parallel and oblique rows of staggered dots;97
7.8;5.8 Conclusion;102
8;6 Branch initiation by global control;104
8.1;6.1 Branch formation: the trigger of backwards waves;104
8.2;6.2 Simultaneous pattern change in distant regions;106
8.3;6.3 No Oliva shell is like another;111
8.4;6.4 The influence of parameters;112
8.5;l6.5 Alternative mechanisms;113
8.6;6.6 A very different pattern generated by the same interaction;114
9;7 The big problem: two or more time-dependent patterns that interfere with each other;118
9.1;7.1 Inherent similarities in complex patterns;118
9.2;7.2 White nonpigmented drop-like pattern on a pigmented background;121
9.3;7.3 Evidence of a sudden extinguishing reaction;123
9.4;7.4 Resolving an old problem with the separate extinguishing reaction;124
9.5;7.5 The next step in complexity: an additional stabilizing pattern;125
9.6;7.6 Branch formation by a temporary stabilization;129
9.7;7.7 Intimate coupling of an enhancing and an extinguishing reaction;132
9.8;7.8 Extinguishing that results from a depletion of resources due to an enhancing reaction;134
9.9;7.9 Related patterns reveal unsolved problems;136
9.10;7.10 Apparently different patterns can be simulated by closely related models;139
9.11;7.11 Conclusion;141
10;8 Triangles;144
10.1;8.1 The crossing solution through the backdoor;145
10.2;8.2 Triangle versus branch formation;148
10.3;8.3 The involvement of three inhibitory reactions;152
10.4;l8.4 Breakdown as a failure of the enhancing reaction;156
10.5;8.5 Conclusion;158
11;9 Parallel lines with tongues;160
11.1;9.1 Survival using a precondition pattern;160
11.2;9.2 Tongue formation: refresh comes too late;163
11.3;9.3 Variations on a common theme;170
11.4;l9.4 Conus textile: tongues and branches on the same shell;172
11.5;9.5 Missing elements, missing links;175
12;10 Shell models in three dimensions;180
12.1;10.1 Mathematical descriptions of shell shape: a brief history;180
12.2;10.2 Elements of shell shape;181
12.3;10.3 The helico-spiral;182
12.4;10.4 The generating curve;184
12.5;10.5 Incorporating the generating curve into the model;184
12.6;10.6 Modeling the sculpture on shell surfaces;187
12.7;10.7 Shells with patterns;192
13;11 The computer programs;200
13.1;11.1 Introductory remarks;200
13.2;11.2 Using the program;200
13.3;11.3 GUIDED TOURS;203
13.4;11.4 Implementation of the interactions;203
13.5;11.5 Numerical instabilities that may cause errors;205
13.6;11.6 Compilers and versions;206
13.7;11.7 Parameters used in the program;207
14;12 Pattern formation in the development of higher organisms;218
14.1;12.1 Hydra, a versatile model system;221
14.2;12.2 Tissue polarity and graded competence;224
14.3;12.3 How to avoid periodic structures during growth;225
14.4;12.4 How to generate structures at a distance: head and foot of hydra;227
14.5;12.5 Induction of adjacent structures;228
14.6;12.6 The evolution of the main body axes;229
14.7;12.7 Gene activation under the control of a morphogen gradient;232
14.8;12.8 Position-dependent activation of several genes;234
14.9;12.9 A problem that the mollusks don't have: the initiation of legs and wings;237
14.10;12.10 Conclusion;241
15;13 Pattern formation in development in which shell-related mechanisms are implicated;244
15.1;13.1 Arrangement of leaves and staggered dots on shells - two similar patterns;244
15.2;13.2 Veins and nerves: the formation of net-like structures;248
15.3;13.3 Chemotactic orientation of cell polarity;252
15.4;13.4 Highly dynamic effects in preparing cell division in budding yeast;255
15.5;13.5 Out-of-phase oscillations in E.coli bacteria for center-finding to determine the plane of cell division;257
15.6;13.6 Dictyostelium: traveling waves at the border to multicellular organisms;258
15.7;13.7 Feather patterns;260
15.8;13.8 Color patterns of feathers;261
15.9;l13.9 Barbs of flight feathers are separated by traveling waves of local signals;263
15.10;13.10 Nerve conduction as a traveling wave phenomenon;264
15.11;13.11 Activation and extinguishing waves in blood coagulation;265
16;References;267
17;Index;276