Index



Babbage, Charles (England, 1791-1871)
     and computers, 1107
     and universality, 1110
Babylonian mathematics
     and calculation, 1149
     and computing pi, 911
     and computing Sqrt, 913
     current influence of, 792
     and definition of math, 859
     and labelling in geometry, 1182
     and math in science, 859
     numbers in, 901
     and primes, 908
     rules in, 875
Babylonians
     and constellations, 1187
     military drill of, 875
     and rule 30 artifacts, 42
Bachelier, Louis (France, 1870-1946)
     and randomness in markets, 1014
Bachet's problem (operator representations), 916
Back-biased zener diodes, 970
Backpropagation
     in neural networks, 1102
Backtracking
     in 3n+1 problem, 904
     in cellular automata, 1089
     and proof searching, 1157
     in rule 30, 605
     in satisfying constraints, 941
     in tiling problems, 217
Backus, John (USA, 1924- )
     and computer languages, 1104
Backus-Naur form, 1104
Backward evolution in CAs, 435
Bacon, Roger (England, ~1219 - ~1292)
     and math in science, 859
Bacteria
     genetic programs of, 1002
     smallest self-replicating, 1179
Bag model
     as mechanistic model, 1026
Bak, Per (Denmark/USA, 1947-[2002])
     and self-organized criticality, 989
Baker, Alan (England, 1939- )
     and Diophantine equations, 1164
Baker's method
     and Diophantine equations, 1164
Baker's transformation (tent map), 150
Balance equations (rate equations), 984
Balanced binary trees, 897, 898
Balanced delimiters, 989
Ball rolling
     in bistable system, 341
     as source of randomness, 970
Balladonia-Caiguna road, 1187
Ballistics tables
     and history of computing, 1107
Balls
     cyclic tag systems made with, 895
     packing of, 349, 986
Bamboos
     growth of, 1004
Banach-Tarski result
     in set theory, 1154
Bands
     in Moire patterns, 1078
Bandwidth
     in perception, 1079
     of radio signals, 1188
Banks, E. Roger (USA, 1944- )
     and 1D universal CA, 1115
     and 2D universal CA, 1117
Barnacles
     patterns on, 385
Barnsley, Michael F. (England/USA, 1946- )
     and parameter space sets, 1006
     and pictures of ferns, 1005
Base 1 (unary), 560, 1070
Base 2 (binary), 116
     and chaos experiments, 919
     history of, 902
     as natural notation, 1182
     in practical computers, 1108
Base 6
     powers of 3 in, 614, 903
Base 10 (decimal), 116
     and chaos experiments, 919
     powers of 2 in, 614, 749
Base 16 (hex)
     digits of pi in, 912
Base 60
     and history of numbers, 902
Base -2 notation, 902
Bases (number), 116
     complex, 932, 933
     conversions between, 1094
     Fibonacci, 560, 892, 902
     generalized, 902
     locality of powers in, 1093
     and normal numbers, 912
     and substitution systems, 891
Basic forms
     in image compression, 574
Basic language
     and history of computing, 1108
     and register machines, 101
Basins of attraction
     boundaries of, 1101
     for cellular automata, 276
     and phase transitions, 341
Basis functions
     in data compression, 574
Basket star
     nested pattern in, 1008
Batcher, Kenneth E. (USA, 1935- )
     and sorting networks, 1142
Bats
     auditory system of, 1079
Battles
     instabilities in infantry, 1014
Bayesian inference, 595, 1083
Bays, Carter (USA, 1940- )
     and 3D class 4 CAs, 949
bcc (body-centered cubic), 930
     and deformable packing, 988
     Voronoi diagram, 987
BDDs (binary decision diagrams), 1097
Beacons
     extraterrestrial, 836
Beam buckling
     and chaos theory, 971
Bearings
     characteristic shapes of, 1183
Beat notes, 146, 1079
Beatty sequences, 890
Beauty
     see Art
Beaver dams
     as animal artifacts, 1184
Beehives (in Game of Life), 964
Beehives (made by bees), 1011
Beeler, Michael D. (USA, 1944- )
     and 2D Turing machines, 930
Begriffsschrift
     of Frege, 1149
Behaviorism, 1099, 1135
Beilstein database, 1194
Bell, Alexander Graham (USA, 1847-1922)
     and speech sounds, 1080
Bell, David I. (USA/Australia, 1953- )
     and structures in Life, 965
Bell, John S. (England/Switzerland, 1928-1990)
     and quantum mechanics, 1058
Bell curve (Gaussian), 977
Bell Laboratories, xiii
Bell's inequalities, 1064
     history of, 1058
     in quantum field theory, 1065
Belousov, Boris P. (Russia, 1893-1970)
     and oscillatory chemical reactions, 1013
Bénard convection, 1000
     as repetitive behavior, 988
Bendix, Peter B. (USA, 1946- )
     and Knuth-Bendix procedure, 1037
Benford, Frank (USA, 1883-1948)
     and leading digits, 914
Benford's Law, 914
     and powers, 903
Bennett, Charles H. (USA, 1943- )
     and logical depth, 1069
     in Preface, xiii
     and reversibility of computation, 1020
     and sphere packing, 985
Bentley, Wilson A. (USA, 1865-1931)
     and snowflakes, 992
Berger, Robert (USA, 1938- )
     and non-periodic tilings, 943
     and undecidability in tiling, 1139
Berlekamp, Elwyn R. (USA, 1940- )
     and Berlekamp-Massey algorithm, 1087
Berlekamp's algorithm (for Factor), 1192
Bernoulli, Daniel (Netherlands/Switzerland, 1700-1782)
     and molecular theory of gases, 1019
BernoulliB (Bernoulli numbers)
     difficulty of evaluating, 1134
BesselI (modified Bessel function)
     and continued fractions, 914
     and Egyptian fractions, 915
BesselJ (Bessel function)
     asymptotics of, 917
     curve of, 145
     and Klein-Gordon equation, 922
     in Mie scattering, 1133
     and transcendental numbers, 912
BesselY (Bessel function of second kind)
     in Mie scattering, 1133
Beta (volatility)
     of prices in markets, 1015
Beta decay
     parity violation in, 1019
     and quantum field theory, 1057
beta sheets in proteins, 1003
Bethe lattice
     see Tree
Bianchi classification
     for Einstein equations, 1053
Bianchi identity, 1049
Bias
     randomness to avoid, 841, 1192
Bible
     and origins of complexity, 861
     randomness generation in, 968
     and understanding nature, 876
Bibliographic information
     on my papers, 881
     in this book, 850
Bibliometrics
     for axiom systems, 1153
     for cellular automata, 878
Biedenharn-Elliott identity (for 6j symbols), 1055
Bifurcations
     and chaos theory, 972
     and fluid flow, 998
     in rate equations, 984
Big bang model
     and basic cosmology, 1055
     and thermodynamics, 1021
Billiards model, 971, 1022
     and thermodynamics, 446
Billion (as 1,000,000,000), 849
Billowing (in clouds), 1001
Binary alloys, 985
Binary cellular automata, 53
     see also Elementary cellular automata
Binary-coded decimal (BCD), 919
Binary-coded ternary, 560, 1070
Binary counter
     in non-periodic tiling, 219
     pattern made by, 117
     Turing machine acting as, 888
     see also Digit sequences
Binary decision diagrams, 1097
Binary mixtures of circles, 350, 985
Binary numbers, 116
     history of, 902
     see also Base 2
     see also Digit sequences
Binary operators
     axioms for, 805
     and generalized additivity, 952
     number of, 1171
     possible Boolean, 806
Binary power method, 1093
Binary star system
     randomness in, 313
Binary trees
     balanced, 897, 898
     as combinator expressions, 1123
     infinite, 196
     space of possible, 405, 1006
     and symbolic expressions, 897
Binomial (binomial coefficients)
     article of mine on, 882
     and associative CAs, 956
     and balanced parentheses, 989
     and Cantor set, 890
     and computational reducibility, 747
     and continuous CA, 922
     and correspondence systems, 1139
     encoded as integer equation, 1160
     and encodings of arithmetic, 1164
     and entropy of particles in box, 1022
     equations involving, 945
     and Fibonacci, 890
     modulo k, 955
     and nested patterns, 610
     and number of conserving CAs, 1023
     and number of expressions, 897, 1175
     and primitive recursion, 907
     and rule 90 pattern, 870
     and Sierpinski pattern, 931
     and trinomial coefficients, 1091
Binomial distribution
     and basic statistics, 1083
     and pegboard, 312
Biological evolution, 383-399, 1001-1003
     CA idealization of, 391
     compared to technology evolution, 398, 1183
     and definition of life, 824
     and features of proteins, 1003
     and form of DNA sequences, 1184
     and intelligence, 822
     and leaf shapes, 1005
     major new features in, 1003
     optimization strategies in, 985
     of perception, 634, 1105
     and shell shapes, 415
     see also Natural selection
Biological growth, 400-422
     Eden model for, 978
     history of studies of, 1003
     see also Growth
Biological systems
     compared to physical ones, 967
     and definition of complexity, 1069
     and extraterrestrial life, 1179
     organization through partitioning in, 457
     in relativity theory, 1042
     and thermodynamic behavior, 453, 1021
Biology, 383-428
     and argument by design, 861
     attitudes in, 1001
     defining features of, 824
     vs. engineering, 393, 1004
     Gaussian distribution in, 977
     history of complexity in, 1001
     mathematics in, 859
     as molecular engineering, 842
     molecules used in, 1194
     Occam's razor in, 1025
     physics applied to, 1003
     probabilistic models in, 1082
     purposes of systems in, 1185
     randomness applied in, 1192
     randomness seen in, 326, 970
     regularities in, 384
     summary of relations to, 8, 863
     undecidability in, 1138
Biomedical applications, 9, 842
Biomedical devices
     and nanotechnology, 1193
Biomedical image processing, 1076
Biometric data
     randomness in, 970, 1014
Biprism
     and non-periodic tiling in 3D, 943
Birds
     vs. airplanes, 1100
     color vision in, 1075
     nests of as artifacts, 1184
     patterns in flocks of, 1011
     pigmentation patterns of, 426
     songs of, 826, 1180
Birkhoff, Garrett (USA, 1911-1996)
     and equational logic, 1172
Bismuth hopper crystals, 993
Bistable systems, 341
     see also Metastable states
Bit reversal
     systems based on, 125
     in Walsh transforms, 1073
BitAnd (bitwise And)
     in Batcher sort, 1142
     in CA implementation, 865
     integer equation for, 1160
     patterns generated by, 871
     and rule 90 pattern, 870
     and Sierpinski pattern, 931
     and zero boundaries, 951
Bitmaps
     compression of, 560
     images as, 1108
     lines in, 916
BitOr (bitwise Or)
     integer equation for, 1160
     iteration of, 906
     patterns generated by, 871
     and representing integers, 916
     and weighted randomness, 976
Bitpacking
     and cellular automata, 866
Bits
     in numbers, 116
     in practical computers, 1108
     see also Digit sequences
Bitslicing
     and cellular automata, 866
Bitwise functions
     iterated, 906, 921
     and logic in computer languages, 1173
     patterns generated by, 871
Bitwise implementation
     of cellular automata, 866
     of rule 30 center column, 871
BitXor (bitwise Xor)
     and Gray code, 901
     iteration of, 906
     and nim, 939
     patterns generated by, 871
     and representing integers, 916
     and Sierpinski pattern, 931
     sounds from, 1080
Bivalve shells, 1008