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Ilachinski A. — Cellular automata. A discrete universe
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Название: Cellular automata. A discrete universeАвтор: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2001Количество страниц: 842Добавлена в каталог: 19.03.2006Операции: Положить на полку |
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Предметный указатель
Fractal dimension, 26 210 Fractals 25 Fredkin logic gate 314 673 Fredkin reversibility 94 Fredkin's billiard-ball gas model 317 Fredkin, Ed 94 313 665 Free energy 327 331 336 Frieden, Roy 646 Frobenius — Perron construction 208 Frustration 337 431 Garbage bits 315 Garden-of-Eden configurations 48 136 Generalized fractal dimensions 212 Generalized threshold automata 274 Genetic algorithms 583 Genetic algorithms, building-block hypothesis 589 Genetic algorithms, CA rule extraction 591 Genetic algorithms, example 588 Genetic operators 584 Geometrodynamics 688 Godel's Incompleteness Theorem 625 632 679 Graph theory 30 616 Graph theory, adjacency matrix 33 Graph theory, automorphism 617 Graph theory, complexity of a graph 616 Graph theory, examples 32 Graph theory, incidence matrix 34 Graph theory, random graphs 34 Graph theory, trees 48 Greenberg — Hastings model 420 groups 35 Halting theorem 3 131 679 684 Hamiltonian graph 32 Hamiltonian systems 167 171 188 Hamming distance 79 harmonic oscillator 189 Heat-conduction equation 485 Henon map 184 Hexagonal lattice 494 hierarchical structures 443 620 Hodgepodge rule 159 422 Homoclinic points 192 homogeneous functions 330 Homogeneous states 231 Immunology 425 Implicit deterministic structures 228 Incidence matrix 34 Infon 645 Information capacity 28 Information dimension, 210 Information mechanics 643 Information physics 634 643 Information theory 27 603 Information theory, Fisher information 646 Information theory, graph complexity 616 Information theory, mutual information 104 Information theory, Shannon information 616 Information theory, thermodynamics 634 Input-free modular systems 261 Intermittency 397 442 475 Invariance matrix 233 Invariant measures 207 Invertibility versus time-reversal invariance 369 Irreversibility 48 60 75 82 94 170 177 188 216 311 313 372 462 634 672 Irreversible rules 48 216 ISAAC combat model 592 Ising model 332 358 Ising model, mean-field approximation 336 Ising model, one-dimensional 334 Isotropic growth 161 Isotropic peripheral PCA 354 Kac-ring model 458 Kac-ring model, origins of irreversibility 462 Kam theorem 190 KAM torus 192 Kauffman, Stuart 3 51 429 560 563 586 Kink diffusion 391 Kink-annihilation 68 Kink-antikink structures 391 Koch curve 27 Kolmogorov — Sinai entropy 213 Kolmogorov's theorem 548 Korteweg — de Vries equation 92 Landauer, Rolf 311 672 Langton's 98 Langton's self-reproducing loop 573 Langton's self-reproduing loop 164 Langton's vants 580 Langton, Chris 562 683 684 Lattice gas computers 502 Lattice gas models, discrete systems 486 Lattice gas models, equations for macroscopic behavior 493 Lattice gas models, FHP model 492 Lattice gas models, HPP model 489 714 Lattice gas models, short history 488 Laypunov functions 275 LCAU 719 Life32 720 Limit cycles 233 Lindenmeyer systems 576 719 Linear PCA 351 Linear peripheral CA 351 Local conservation laws 95 383 Local structure theory (LST) 98 247 363 Local structure theory (LST), 253 Local structure theory (LST), 254 Local structure theory (LST), 255 Local structure theory (LST), 256 Local structure theory (LST), Bayesian extension 250 Local structure theory (LST), block probability functions 249 Local structure theory (LST), CA action on probability measures 249 Local structure theory (LST), local structure operator 251 Local structure theory (LST), LST for d-dimensional lattices, d > 1 258 Local versus global 558 Localized demons 361 Logic gates 144 311 312 Logic gates, reversible 313 Logical depth 626 Logistic map 177 389 Logistic map, fixed-point solutions 178 Logistic map, limit cycles 180 Logistic Map, universality 181 Louiville's theorem 476 Lyapunov dimension 213 Lyapunov exponents 201 Lyapunov exponents, CA analogs 206 Lyapunov exponents, information-theoretic interpretation 205 Lyapunov functions 521 Lyapunov functions, threshold CA rules 274 Majority rules 280 MapleV 722 Marginal stability 406 Margolus 129 317 375 676 713 Margolus neighborhood 320 Mathematica 722 Maxwell — Boltzman distribution 483 Maxwell's demon 310 635 McCulloch — Pitts artificial neuron 510 Mean-field approximation 101 530 Mean-field theory 338 349 358 Measure entropy 215 Metastability 528 Metric entropy 213 Metric function 24 Metrizability 25 Metropolis algorithm 359 microcanonical ensemble 35 359 Microscopic reversibility 354 Minimal basis 313 Minimal DFA 300 Minimization algorithm 300 Minsky, Marvin 509 662 Mobile CA 457 Moebius function 243 Molecular chaos 495 Momentum flux tensor 466 Monte Carlo dynamics 328 Moore neighborhood 49 Multi-layered perceptrons 536 550 Multithreshold rules 284 Myhill — Nerode theorem 300 n-dimensional discrete maps 203 N-k landscapes 430 586 NAND logic gate 313 Natural topology 107 Navier — Stokes equations 466 483 500 NETtalk 552 Neural networks, ADALINE 514 Neural networks, adaptve resonance 555 Neural networks, biological origins 510 Neural networks, Boltzman machines 531 Neural networks, Boltzman machines, learning rule 534 Neural networks, connection with CA 508 Neural networks, Hebbian learning rule 512 Neural networks, Hopfield model 518 Neural networks, Hopfield model, capacity 524 Neural networks, Hopfield model, energy function 520 Neural networks, Hopfield model, learning rule 522 Neural networks, Hopfield model, pseudo-code 527 Neural networks, Hopfield model, spurious attractors 524 Neural networks, McCulloch — Pitts model 511 Neural networks, model development 546 Neural networks, NETtalk 552 Neural networks, overview 507 Neural networks, stochastic models 528 Neural networks, supervised learning 555 Noether's theorem 378 Non-homogeneous CA 51 Non-monotonic behavior 598 Noncomputability 681 NP-complete problem 532 624 One-dimensional CA 41 53 One-dimensional CA, algebraic properties 237 One-dimensional CA, algebraic properties cycle length distribution 242 One-dimensional CA, algebraic properties, rule R90 238 One-dimensional CA, blocked space-time patterns 70 One-dimensional CA, blocking transformations 66 One-dimensional CA, critical-like behavior 86 One-dimensional CA, filter automata 92 One-dimensional CA, langton's 98 One-dimensional CA, legal rules 44 One-dimensional CA, majority rules 280 One-dimensional CA, notation 41 One-dimensional CA, parity rule FA 92 One-dimensional CA, Park's glider-gun 91 One-dimensional CA, particle-like behavior 87 One-dimensional CA, reversible, rules 94 One-dimensional CA, rule codes 44 One-dimensional CA, rule R110 661 One-dimensional CA, rule R150 56 One-dimensional CA, rule R18 68 One-dimensional CA, rule R90 55 One-dimensional CA, rule-space parameterization 98 One-dimensional CA, sandpile model 438 One-dimensional CA, solitons 91 One-dimensional CA, space-time patterns 53 One-dimensional CA, space-time patterns, behavioral classes 63 One-dimensional CA, space-time patterns, difference plots 64 One-dimensional CA, space-time patterns, irregular growth 59 One-dimensional CA, space-time patterns, random seeds 59 One-dimensional CA, space-time patterns, simple seeds 54 One-dimensional CA, spatial and temporal measure dimensions 223 One-dimensional CA, totalistic rule T20 (r=2) 89 One-dimensional CA, totalistic rule T88 (r=3) 89 One-dimensional CA, Wolfram's behavioral classification 98 One-dimensional random walk 670 Order parameter 339 Parable 661 Parse trees 297 Partition function 326 333 530 Partitioning CA 374 715 Pattern entropy 395 Perceptions (book) 509 Perceptrons 512 Perceptrons, learning rule 514 Perceptrons, multi-layered 536 Percolation 332 344 355 433 Period doubling 184 185 357 389 Periodicity of temporal sequences 229 Peripheral PCA 345 Peripheral PCA, isotropic 354 Peripheral probabilistic CA 345 Phase space 170 211 Phase transition 98 325 332 346 355 357 531 691 Physical entropy 626 Physics and information 608 632 Poincare maps 168 Pomeau — Manneville intermittency 397 Power spectra 304 394 Power spectra, Li's algorithm 306 Power spectra, sandpile models 441 Predictability 175 Pregeometry 639 Probabilistic CA 50 Programmable matter 713 PSPACE-complete problem 624 Pullback-technique 203 Pumping lemma 304 Push-down automata 296 Quantum CA 51 406 Quantum CA, QCA-I 407 Quantum CA, QCA-II 411 Quantum measurement problem 635 Quantum mechanical computers 673 Random Boolean networks 429 Random graphs 34 654 Random mappings 435 RAP1 510 716 Rational canonical form 263 Reaction-diffusion systems 419 Recursive growth models 577 Reductionism 608 Regular language complexity 302 Regular languages 293 Renyi entropy 218 Renyi information 212 Replica method 338 Restricted totalistic rules 446 Reversible CA 94 369 606 652 Reversible CA, elementary reversible CA (ERCA) 376 Reversible CA, historical overview 371 Reversible CA, synthesis techniques 372 Reversible CA, synthesis techniques, conserved landscape permutations 374 Reversible CA, synthesis techniques, Fredkin's construction 374 Reversible CA, synthesis techniques, partitioning 375 Reversible computation 50 309 315 638 Reversible computation, Feynman's challenge 638 Reversible computers 672 Reversible logic circuit 316 Reversible logic gate 313 674 Reversible rules 50 94 Reynold's number 469 Reynold's number, scaling 505 Rings 36 Roots of unity 243 Sandpile CA model 437 Sandpile CA model, d-dimensional 440 Sandpile CA model, one-dimensional 438 Sandpile CA model, power-law scaling 441 Santa Fe Institute 4 607
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