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Schroeder M.R. — Schroeder, Self Similarity: Chaos, Fractals, Power Laws
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Название: Schroeder, Self Similarity: Chaos, Fractals, Power LawsАвтор: Schroeder M.R. Аннотация: Readers of James Gleick's 1989 bestseller, Chaos, The Making of a New Science, will find the revolution predicted there in full swing in this advanced look at "self-similarity, ' ' one of chaos theory's most appealing applications. Self-similarity in computer graphics yields the awesome fractal mountain patterns that have made chaos a visible theory for many nonmathematicians. Readers with good command of calculus and some physics will appreciate how far chaos theory has penetrated theoretical physics, biology and the practice of research as described in puns, illustrations and puzzles by this 20th-century Lewis Carroll. Without those skills, however, readers may stand like Alice before a small door that opens on strange new wonders of the physical world, the extended horizons of number theory and advanced math recreation. Schroeder is a professor of physics at Goettingen University in Germany.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1991Количество страниц: 432Добавлена в каталог: 09.04.2008Операции: Положить на полку |
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Предметный указатель
Diffraction 44 304 315 Diffraction from fractals 44 233 Diffusion 198 352 381 Diffusion constant 143 Diffusion equation 143 Diffusion-limited aggregation 196 198 201 232 Digital chip 151 Digital filter 266 Digital sundial 181 Digital system 98 Digital-to-Analog Converter 95 Digitization 57 Dimensionless number 70 Direct product 181 239 Discrete logarithm 79 Disordered system 302 366 Dissimilarity 61 75 77 Distribution of galaxies 152 155 356 DLA see “Diffusion-limited aggregation” Doenitz, K. 33 Douady, A. [DH 82] [DH [Dou 296 298 299 Double star 25 Dougherty, A. [SWGDRCL 86] Drag force 70 Dragon curve 47 Dress, A.W.M. [DGJPS 85] 386 Dressed winding number 175 331 334 Drift 381 Du, B.-S. [Du 84] 166 Duneau, M. [DK 85] [KD Duration of the game 210 Dynamic system 166 D’Antonio, P. [D’An 90] Earth 338 Eckhardt, D.H. [JER 90] Eckmann, J.-P. [CE 80] Economics 34 EEG see “Electroencephalogram” Effective velocity 173 Eggleton, R. B. 147 Eggleton, R.B. [EG 88] Eider’s function 336 Eiffel, G. 19 Eightfold symmetry 318 Einstein, A. [Ein 05] 1 3 5 139 140 143 144 155 189 302 334 Einstein, J. 3 Eldely, A. [Erd 54] Electric circuit 225 Electrical breakdown 197 Electrical conduction 227 Electrical potential 198 Electroencephalogram 223 Electrolytic deposition 233 Electromagnetic cavity 69 189 electromagnetic field 69 189 Electromagnetism 106 Electron mass 106 113 Electrostatics 299 Elliptic integral 258 Elsner, V. [Els 85] Embedding dimension 224 Embedding space 350 Emde, F. [JE 51] Energy barrier 123 Energy dissipation 63 Energy fluctuation 114 Energy loss mechanisms 69 entropy 35 203 206 222 Entropy function 128 191 Equation of motion 66 Equipartition of energy 144 Equipotential surface 198 Equivalent number 343 392 Error probability 128 151 Error-free computing 88 Error-free transmission 151 Escher, M.C. [Esc 71] 17 361 Euclidean scaling 14 137 237 Euler’s infinite product 98 Even period length 287 Exactly solvable model 366 Expected duration 146 210 Expected gain 146 148 Experimental aesthetics 70 External angle 298 External field 390 Eykolts, R. [EU 86] Fackler, O. [TKFFHKMM 89] Fair coin tossing game 146 148 Falconer, K.J. [Fal 87] 182 Family, F. [FL 84] Farey tree 2 336 339 Farmer, J.D. [Far 82] [Far 185 Fast algorithm 385 Fast Fourier Transform 239 Fat fractal 183 Fatou set 39 Fatou, P. 39 298 Fazzini, T. [BBFT 89] Fechner, G.T. 70 Feder, J. [HJF 87] 213 Feigenbaum constant 2 280 Feigenbaum, M. 274 Feigenbaum, M.J. [Fei 79] [Fei Fein, A.P. [FHG 85] Feller, W. [Fel 68] Felske, D. [TKFFHKMM 89] Ferguson, J.F. [AZL...89] Feynman, R. 112 FFT see “Fast Fourier transform” Fibbonacci, L. [Fib 1202] Fibonacci nim 53 Fibonacci number system 49 55 91 171 256 306 308 328 337 393 Fibonacci, L. 85 304 Fifth force 33 106 Filled-in Julia set 297 Finite field 79 Finite precision 52 294 Finite-size scaling 354 Finite-state algorithm 258 Finite-state automata 291 First digit distribution 116 Fisher, D.E. [Fis 90] Fisher, E. [AZL...89] Fisher, M. 357 Fivefold symmetry 301 318 325 328 Fixed point 240 268 Fleckinger-Pelle, J. [LF 88] 41 Forbidden symmetry 301 315 Four-dimensional space 41 Fourier spectrum 122 Fourier transform 133 158 266 Fractal boundary 244 Fractal coast 213 Fractal colloid 235 Fractal diffraction 44 Fractal diffraction gratings 236 Fractal dimension 16 153 160 192 193 202 320 354 363 Fractal growth 198 Fractal inner surface 236 Fractal interface 225 228 Fractal landscape 137 Fractal lattice 350 Fractal paradox 15 Fractal perimeter 48 Fractal phenomenon 389 Fractal subset 193 Fractal support 201 Fractal tile 14 Fractional differentiation 132 Fractional exponent 103 115 Fractional integration 132 Fracton 43 Fracture 230 Fraunhofer diffraction 44 Frederick II 84 Free of scale 31 Frequency plane 133 Frequency pulling 171 Frequency ratio 98 171 175 334 Frequency response 72 73 74 Frequency vector 133 Friction 69 151 Friedrich II [Fri 1240] Fukano, Y. [INF 85] [INF Fuller, R.B. 20 Fundamental physical constants 113 Galileo 63 64 67 105 163 Galton board 147 Galton, F. 147 Gambler’s ruin paradigm 145 gambling 128 129 148 149 150 151 152 168 207 208 Game of life 373 Garden of Eden pattern 382 Gardner, M. [Gar 70] [Gar [Gar [Gar [Gar Gauss map 51 Gauss, C.F. 70 117 124 171 215 Gaussian distribution 73 133 157 Gaussian noise 129 Gaussian plane 39 GCD see “Greatest common divider” Gedanken experiment 112 Geisel, T. [GZR 87] 125 General relativity 41 Generalized dimension 203 Generalized entropy 203 Generating function 145 266 Genetic drift 382 Genghis Khan 33 Geometric distribution 188 George III 215 Gerhardt, M. [DGJPS 85] Gervois, A. [DGP 78] Gibbs, J.W. 206 Gierer, A. 382 Gilbert, E.N. [Gil 58] Gilbert, W.J. [Gil 84] Gleick, J. [Gle 87] Global warming 131 Goedel, K. 177 Golden angle 339 Golden mean 50 51 52 54 55 91 95 226 304 316 319 324 325 329 337 339 343 394 Golden-mean slope 56 Gollub, J.P. [FHG 85] [SWGDRCL Gorman, M.R. [AZL...89] Gottlob, D. [SGS 74] Graham, R.L. [GLL 78] Graph theory 363 Grassberger, P. [Gra 81] [GP [Gra [Gra 233 276 352 Gratias, D. [SBGC 84] Gravitational attraction 33 Gravitational lens 155 Gravity 65 67 106 Gray, code 12 282 Greatest common divider 237 Greedy algorithm 210 Greenhouse effect 131 Greer, J. [AZL...89] Gregory — Leibniz series 257 Grimmett, G. [Gri 89] Grossmann, S. [GT 77] [Gro 275 Growth parameter 268 274 Growth rate 128 201 Gruenbaum, B. [GS 87] Guy, R.K. [BCG 82] [EG 147 Gwinn, E.G. [GW 87] Gyromagnetic ratio of the electron 302 Hadamard transform 239 Hadamard, J. 295 Haken, H. [Hak 78] Haldane, J.B.S. [Hal 28] 9 63 Half integration 132 Halmos, P.R. [Hal 74] 82 Halsey, T.C. [HJKPS 86] 205 Hamiltonian systems 125 256 Hammer, P. [AZL...89] Hansen, B.L. [AZL...89] Hardy, G.H. [HW 84] Harmonic of an orbit 284 Harris, R. [TKFFHKMM 89] Harris, S. [Har 77] Harwit, M. [HS 79] Hasinger, G. [HLSTLW 86] Hausdorff dimension 2 9 15 137 141 153 177 179 181 201 207 213 216 229 230 276 334 388 391 Hausdorff, F. 2 10 Hawking, S. [Haw 88] 98 Hearing research 44 122 Heisenberg, W. 107 Heisenberg’s uncertainty principle 63 73 112 Henon attractor 255 Henon, M. [Hen 76] [Hen 169 170 Henon’s map 253 Hensel code 88 Hentschel, H.G.E. [HP 83a] [HP [HP 232 Henze, H. 315 Herman, R. [AH 48] 115 Hermite, C. 7 242 Heutmaker, M.S. [FHG 85] Hierarchical construction 225 Hierarchical lattice 362 Hierarchical neighborhood 364 Hierarchical structure 88 Hilbert curve 2 10 Hilbert envelope 108 Hilbert space 113 Hilbert space-filling curve 282 Hilbert transform 108 Hilbert, D. 40 Hildebrand, J.A. [AZL...89] Hinkle, E.B. [SHJ 88] Hinrichsen, E. [HJF 87] Hirzebruch, F. 150 Hofstadter, D.R. [Hof 80] 237 Hogarth, W. 215 Holes on all scales 43 Hologram laser speckle 73 Holography 114 147 Holzfuss, J. [LH 86] Homogeneous power laws 33 103 108 122 Homograph 37 Hu, B. [Hu 85] Hubbard, J.H. [DH 82] [DH 296 298 Hubble, E. 345 Human hearing 44 85 97 Human perception 34 38 Human speech production 44 Hunt, F.V. [HBM 39] Hurd, A.J. [MH 87] Hurst exponent 130 137 Hurst, H.E. [HBS 65] 129 131 Hutton, E.F. 121 Huygens principle 171 Huygens, C. 171 Huygens, Ch. [Huy 1673] Hydrodynamic instability 200 Hydrodynamics 68 70 372 Hyperbolic distribution 124 Hyperbolic fixed point 256 Hyperbolic law 35 108 113 125 Hyperbolic map 51
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