Computing in Nonlinear Media and Automata Collectives

by Adamatzky; Andrew

• ISBN13: 9780750307512
• ISBN10: 075030751X
• Format: Hardcover
• Copyright: 2001-06-22
• Publisher: CRC Press

Summary

Gives an account of new ways to design massively parallel computing devices in advanced mathematical models, and from unconventional materials, for example chemical solutions, bio-polymers and excitable media. Explains how to design computing devices in nonlinear media.

Author Biography

Dr Andrew Adamatzky is a faculty member at the University of the West of England, Bristol, United Kingdom

Table of Contents

Preface	p. ix
Reaction-diffusion, excitation and computation	p. 1
Unconventional computing	p. 1
Waves in reaction-diffusion and excitable media	p. 4
Cellular automata	p. 11
Modelling reaction-diffusion and excitable media	p. 18
Computing in nonlinear active media	p. 26
Reaction-diffusion media with smart molecules	p. 33
Subdivision of space	p. 35
Voronoi diagram	p. 36
Planar Voronoi diagram	p. 37
Discrete Voronoi diagram	p. 39
Bisectors	p. 40
O(n)-algorithm	p. 45
O(1)-algorithm	p. 50
Quality of the bisectors	p. 54
Generalized Voronoi diagram	p. 56
Inversion of Voronoi diagram	p. 60
Skeleton	p. 66
Chemical processors for tesselation and skeletonization	p. 69
Grass fire in Belousov-Zhabotinsky reaction: Rambidi's approach	p. 69
Chemical processors for the approximation of Voronoi diagrams and skeletons	p. 71
Voronoi diagram in a lattice swarm	p. 75
One experiment with Tapinoma karavaevi	p. 75
Probabilistic diffusion	p. 77
Collectives of automata	p. 77
Analysis of algorithms	p. 82
Shapes of Voronoi diagram	p. 86
Rational geography	p. 91
Convex hull	p. 92
Topology-based algorithm	p. 98
Two-state algorithm	p. 99
Excitable computation	p. 102
Computation on and with graphs	p. 105
Shortest paths and trees	p. 105
Random walk, electricity and tree approximation	p. 108
Field computing on graphs	p. 109
Computation of shortest paths in cellular automata	p. 112
Computation of trees by neurites	p. 122
Spanning trees on random lattices	p. 129
Construction of graphs by diffusive families of ants	p. 135
Graph dynamics in real ants	p. 137
Ant-approximation of planar proximity graphs	p. 140
Exploring the complex space	p. 145
Load balancing in communication networks	p. 153
Diffusion-like algorithms	p. 154
Ants on the net	p. 157
How good is ant diffusion at balancing communication networks?	p. 162
Chemical processors that compute shortest paths	p. 165
Computational universality of nonlinear media	p. 171
Artificial and natural universality	p. 173
Architecture-based universality	p. 175
Sand-piles	p. 175
Mass-transfer-based gates	p. 180
Wave gates	p. 181
Employing collisions: billiard ball model	p. 183
Game of Life	p. 185
The excitable lattice	p. 186
Minimal particle-like waves	p. 187
Particle guns: the generators of the particle-like waves	p. 191
Collisions and interaction gates	p. 197
Reflectors, counters and registers	p. 209
Excitation or Life?	p. 213
Search for universality	p. 215
Solitons, light bullets and gaussons	p. 216
Solitons	p. 216
Light bullets	p. 219
Gaussons	p. 222
Breathers	p. 224
When are breathers born?	p. 227
How do breathers collide?	p. 228
Collision of breather with impurity	p. 230
Collision gates in DNA	p. 232
Scheibe aggregates and excitons	p. 243
Microtubule computing	p. 245
Automata models of Scheibe aggregates and microtubules	p. 246
Localizations in granular materials	p. 250
Worms in liquid crystals and automata lattices	p. 252
Reaction-diffusion and active particles	p. 259
Emergence of computation in excitable lattices	p. 264
Three types of excitation rules	p. 265
Threshold excitation rule	p. 266
Interval excitation rule	p. 266
Vector excitation rule	p. 267
Relations between the rules	p. 267
Lattices with interval excitation	p. 268
Basics of classification	p. 268
Findings	p. 268
Analysis of excitation dynamic	p. 269
Morphological diversity	p. 273
Interval excitation controllers for mobile robots	p. 275
Architecture of the excitable controller	p. 276
Activity patterns and vector fields	p. 278
Taxonomy of robot trajectories	p. 284
Robot's performance and excitation intervals	p. 287
Fault tolerance of interval excitation lattice controllers	p. 287
Simulated controllers in real robots	p. 290
Real-life candidates for excitable controllers	p. 290
Lattices with vector excitation rules	p. 295
[lambda]-like parameter of excitation rules	p. 296
Initial conditions	p. 297
Characteristics of the global dynamic	p. 297
Morphological characteristics	p. 298
Morphological classification	p. 299
How initial conditions influence the structure of the classes	p. 302
Morphological diversity	p. 307
Excitation generators	p. 314
Integral dynamics	p. 320
Parametric classification	p. 322
Computation in excitable lattices	p. 332
Specialized computation: image transformation	p. 334
Universal computation	p. 344
Parametrizations of computational abilities	p. 344
Motility-based classification of excitable lattices with vector excitation rules	p. 345
Bibliography	p. 357
Index	p. 389
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