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Ilachinski A. — Cellular automata. A discrete universe
Ilachinski A. — Cellular automata. A discrete universe

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Название: Cellular automata. A discrete universe

Автор: Ilachinski A.

Аннотация:

Cellular automata are a class of spatially and temporally discrete mathematical systems characterized by local interaction and synchronous dynamical evolution. Introduced by the mathematician John von Neumann in the 1950s as simple models of biological self-reproduction, they are prototypical models for complex systems and processes consisting of a large number of simple, homogeneous, locally interacting components. Cellular automata have been the focus of great attention over the years because of their ability to generate a rich spectrum of very complex patterns of behavior out of sets of relatively simple underlying rules. Moreover, they appear to capture many essential features of complex self-organizing cooperative behavior observed in real systems.
This book provides a summary of the basic properties of cellular automata, and explores in depth many important cellular-automata-related research areas, including artificial life, chaos, emergence, fractals, nonlinear dynamics, and self-organization. It consists of 12 largely self-contained chapters. The last chapter presents a broad review of the speculative proposition that cellular automata may eventually prove to be theoretical harbingers of a fundamentally new information-based, discrete physics. Designed to be accessible at the junior/senior undergraduate level and above, the book will be of interest to all students, researchers, and professionals wanting to learn about order, chaos, and the emergence of complexity. It contains an extensive bibliography and provides an annotated listing of cellular automata resources available on the World Wide Web.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 842

Добавлена в каталог: 19.03.2006

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Предметный указатель
"bucket of dust"      639
"it from bit"      640
1/f noise      437 441
3D Life rule      151
3D Life rule, analogs of 2D Life patterns      154
Abstract automata      38
Abstract automata, alphabet      38
Abstract automata, formal languages      38
Abstract automata, formal languages, example      39
Abstract automata, strings      38
ADALINE      514
Additive invariants      378
Adjacency matrix      33
Agent-based models      564
Agent-based models, versus traditional AI      566
algorithmic complexity      624
Algorithmic randomness      624
Algorithmically incompressible      625
AND logic gate      313
Anthropic principle      685
Area-preserving map      193
Artificial life      604 708
Artificial life, combat models      592
Artificial life, Lindenmeyer systems      576
Artificial life, overview      557
Artificial life, SWARM      568
Associative memory      518
Autonomous agent      565
Autoplectic systems      86
Backpropagation      540
Backpropagation, pseudo-code      544
Bak, Per      437
Baker — Campbell — Hausdorff series      653
Basin complexity      272
BBMCA rule      321
Bell's theorem      677
Belousov — Zhabotinski reaction      15 419 612 630
Bernoulli shift map      172
Billiard-Ball model (BBM)      317 673 681
Black holes      636
Block blentropy      216
Block probability      217 249 720
Blocking transformation      66 70
Boids      561
Boltzman distribution      326
Boltzman's equation      459 475 494
Boltzman's H-theorem      459 479
Boolean function      312 429 430 516
Boolean logic gate      318
Boolean satisfiability      624
Bottom-up      558
boundary conditions      41
Box-counting algorithm      213
Brillouin, Louis      310
Busy Beaver function      681
CA and formal languages      298
CA lab      717
CA models of combat      457
CA Over $\mathcal{F}_{p}$ (p Prime)      245
CA phase space      46 215
CA simulations of spin models      358
CA-based cosmogony?      694
CA-like representation of real-valued maps      198
CAM-6      128 510 713
CAM-8      714
CAM-PC      718
Canonical distribution      385
Cantor set      20 47
Cantor's diagonal argument      24
CAPOW      718
Capra, Fritjof      608
Cardinality      23
Cartesian product      23
CellMaster      718
Cellsim      718
Cellular automata      4
Cellular automata, collective behaviors      10
Cellular automata, computation      6
Cellular automata, Conway's Life example, (short)      13
Cellular automata, embodiments of paradigm shift      608
Cellular automata, finite lattice dynamics      47 75
Cellular automata, formal language theory      298
Cellular automata, fundamental physics      9
Cellular automata, lattice-gas example      15
Cellular automata, one-dimensional examples      9
Cellular automata, pattern formation      8
Cellular automata, powerful computational engines      7
Cellular automata, simulation tools      8
Cellular automata, topological characterization      46
Cellular automata, why study CA?      7
Cellular automata, Wolfram's behavioral classification      98
Chaos      167 172 177 182 192 204 390
Chaotic attractors      175
Chapman — Enskog expansion      497
Chomsky language hierarchy      294
Church — Turing thesis      682
Church's Theorem      679
Circle map      387 397
Circulant matrix      237
Collective sorting      561
Collectivism      609
Color plates      156
Combat models      592
Combinatorial hierarchy      641
Complex systems      2 611
Complex systems, chronology      3
Complex systems, on-line resources      722
complexity      611
Complexity as information      615
Complexity engineering      248
Complexity science      607 611 629
Complexity, algorithmic complexity      624
Complexity, computational complexity      623
Complexity, dynamic complexity      614
Complexity, graph complexity      616
Complexity, hierarchical systems      620
Complexity, logical depth      626
Complexity, simplicial complex      619
Complexity, static complexity      614
Complexity, thermodynamic depth      627
Complexity, topological complexity      617
Computability      176 624
Computability and physics      678
Computation and phase transitions      682
Computational complexity      623
Computational irreducibility      680
Connected graph      32
Connection Machine      716
Conservative logic circuits      315
Context-free grammar      296
Context-free languages      296
Continuity equation      465 482 496
Conway's Life Rule      3 13 129 631 720
Conway's Life Rule, proof of universality      141
Conway's Life Rule, stochastic version      363
Conway's Life Rule, three-dimensional version      151
Conway's Life Rule, What's so Special About Life?      131
Conway's Life Rule, zoology      132
Conway's Life Rule, zoology, eaters      136
Conway's Life Rule, zoology, flotillas      136
Conway's Life Rule, zoology, garden-of-Eden configurations      136
Conway's Life Rule, zoology, glider shuttle      136
Conway's Life Rule, zoology, glider-glider collisions      136
Conway's Life Rule, zoology, gliders      135
Conway's Life Rule, zoology, puffer trains, guns and breeders      138
Conway's Life Rule, zoology, R-pentomino      135
Conway's Life Rule, zoology, simple seeds      133
Conway's Life Rule, zoology, spaceships      135
Conway, John      3 6
Cooperative structures      581
Correlation dimension, $D_{C}$      211
Correlation function      73 334 442
Coupled-map lattices      51 386
Coupled-map lattices, CA approximations      401
Coupled-map lattices, CA approximations, first-order      404
Coupled-map lattices, CA approximations, higher-order approximations      405
Coupled-map lattices, entropy      395
Coupled-map lattices, homogeneous solutions      387
Coupled-map lattices, inhomogeneous initial states      388
Coupled-map lattices, logistic equation      443
Coupled-map lattices, pattern distribution      394
Coupled-map lattices, quantitative measures      393
Coupler link rules (for SDCA)      444
Creutz's demons      361
Critical behavior      325 344
Critical exponents      329 346
Cubic lattice      151
Cycle length      243
Cyclic CA      158
Cyclic states      280 288
Cyclotomic polynomial      243
Decoupler link rules (for SDCA)      444
DeMorgan laws      23
Descendent forcing structures      433
Detailed balance      328 353—355
Deterministic finite automaton (DFA)      300
Deterministic randomness      175
Difference patterns      64
Difference space-time pattern spreading rate      100
Digital mechanics      639 666
DIL systems      579
Dimensional shadowing      649
Dimer problem      270
Discrete dynamics lab      719
Discrete Green function      64
Discrete physics      610 638
Discrete space-time      653 663 688
Dissipative systems      170
DOL systems      576
Dresden, Max      xxiii 460
Dynamical entropy      396
Dynamical rules, additive rules      45
Dynamical rules, aditive rules      48
Dynamical rules, BBMCA rule      321
Dynamical rules, billiard-ball rule      320
Dynamical rules, brain CA      162
Dynamical rules, CCA rule      158
Dynamical rules, chaotic      102
Dynamical rules, critical rules      406
Dynamical rules, deduction of properties      225
Dynamical rules, dependence on lattice topology      107 259
Dynamical rules, dependence on lattice topology, general solution in $\mathcal{F}[g]$      261
Dynamical rules, dependence on lattice topology, natural topology      260
Dynamical rules, dependence on lattice topology, simplifications in $\mathcal{F}[2]$      269
Dynamical rules, dependence on lattice topology, [3:3:3] profiles      112 114
Dynamical rules, faders CA      163
Dynamical rules, hodgepodge rule      159
Dynamical rules, legal rules      44
Dynamical rules, majority rules      280
Dynamical rules, minimally diluted deterministic rules      355
Dynamical rules, multithreshold rules      284
Dynamical rules, notation      40
Dynamical rules, nucleating rules      125
Dynamical rules, outer-totalistic rules      45
Dynamical rules, parity rule FA      92
Dynamical rules, Park's glider-gun      91
Dynamical rules, percolating rules      125
Dynamical rules, reversible rules      50
Dynamical rules, rule codes      44
Dynamical rules, rule composition      43
Dynamical rules, rule R110      661
Dynamical rules, rule R150      56
Dynamical rules, rule R178      298
Dynamical rules, rule R18      68 236
Dynamical rules, rule R30      84
Dynamical rules, rule R90      55 238
Dynamical rules, state transition graph      298
Dynamical rules, stepping stone CA      160
Dynamical rules, totalistic rules      44
Dynamical rules, traffic CA      157
Dynamical rules, voting rules      124
Dynamical system theory      167
Dynamical system theory, Bernoulli shift map      172
Dynamical system theory, conservative systems      171
Dynamical system theory, conservative systems, integrability      188
Dynamical system theory, conservative systems, phase protraits      190
Dynamical system theory, conservative systems, standard map      193
Dynamical system theory, dissipative systems      170
Dynamical system theory, Hamiltonian systems      171
Dynamical system theory, Henon map      184
Dynamical system theory, invariant measures      207
Dynamical system theory, logistic map      177
Dynamical system theory, Lyapunov exponents      201
Edge-of-chaos      106 562 683
Effective dimensionality, $D_{effec}$      455
Effective-measure complexity      219
EINSTein combat model      592
Einstein, Podolsky and Rosen (EPR) paradox      677
Elementary CA      71
Elementary CA, finite lattices      75
Elementary CA, global properties      75
Elementary CA, global properties, cyclic states      76
Elementary CA, global properties, entropy      80
Elementary CA, global properties, Garden-of-Eden states      76
Elementary CA, global properties, stability      79
Elementary CA, global properties, statistical ensembles      80
Elementary CA, global properties, transient states      76
Elementary CA, infinite lattices      82
Elementary CA, local properties      71
Elementary CA, local properties, correlation function      73
Elementary CA, local properties, density      71
Elementary CA, local properties, mean-field approximation of density      73
Elementary CA, rule R110      87 661
Elementary CA, rule R150      56
Elementary CA, rule R18      68
Elementary CA, rule R22      83
Elementary CA, rule R30      84
Elementary CA, rule R90      55
Elliptic points      191
Emergence      14 400 560 606 628 631
Encryption      95
entropy      100 302 637
Entropy, dynamical entropy      396
Entropy, formal language theory      302
Entropy, pattern entropy      395
Enumeration of limit cycles      233
Euler totient function      243
Euler's equation      465 482 496
Extension field      242
Feedback catastrophe      359
Feedback shift register      45 236
Feigenbaum constant      182
Feigenbaum, Mitchell      177 181
Field theory      647
Field theory, reformulated as a CA: I      648
Field theory, reformulated as a CA: II      651
Field theory, reformulated as a CA: III      654
Fields      36
Filter automata      92
Filter automata, parity rule      92
Finite automata      38 294
Finite lattice dynamics      47 75
Fisher information      646
Fitness landscape      585
Flicker noise      442
Fluid dynamics      463
Forcing loops      433
Forcing structures      432
Formal language theory      292
Formal language theory, pumping lemma      304
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