INDEX

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V

V1 visual cortex, 1075
Vacuum Einstein equations, 536, 1053
Vacuum fluctuations, 540, 1062
     and Bell's inequalities, 1065
     as source of decoherence, 1063
Vacuum polarization, 1062
Vacuum tubes
     1/f noise in, 969
     and Nand, 1173
     randomness in, 303, 971
Valuation functions
     for trees, 916
Valuation tables (truth tables)
     in operator systems, 801, 1170
Value sets of polynomials, 1161
van der Corput, Johannes G. (Netherlands, 1890-1975)
     and digit reversal sequences, 905
van der Pol, Balthazar (Netherlands, 1889-1959)
     and history of chaos, 971
van der Pol equation, 922, 971
van der Poorten, Alfred J. (Australia, 1942- )
     and nested digit sequences, 913
van der Waerden's Theorem
     in Ramsey theory, 1068
Vants (2D Turing machines), 930
Variables
     in mathematical logic, 1150
     notation for, 1182
     in programs in notes, 854
     and pure functions, 1121
     scoping of, 1152
Variance
     and Central Limit Theorem, 976
Variational derivatives
     in path integrals, 1061
Variational principles
     as constraints, 940
     for gravity, 1052
     and notion of purpose, 1185
Vauban star forts
     nested architecture of, 874
VAX 11/780 computer
     my use of, 854, 864
VC (Vapnik-Chervonenkis) dimension, 1102
Vector fields
     topological defects in, 1045
Vector potential
     and gauge invariance, 1045
Vector quantities
     conservation of, 1024
Vectors
     as generalizing numbers, 1168
Vedic poetry
     and Fibonacci numbers, 891
Vegetation bands
     maze-like patterns in, 1013
Veins
     in leaves, 404
     and transportation in cities, 1014
Venn, John (England, 1834-1923)
     and randomness in digits of pi, 879, 912
Venn diagrams, 1171
Ventifacts (wind-sculpted forms), 1001, 1183
Venus
     and extraterrestrial life, 1179
Verbal communication, 1181
Verbal processing in brains, 1181
Verbs
     in human languages, 1103
     in math notation, 1182
Verhulst equation
     and iterated maps, 918
Verifiability
     of models, 366
     of ultimate theory of physics, 469
Verification
     and theorems about programs, 1168
Verilog
     and logic operations, 1173
Vertex coloring (maximum clique)
     and discrete packing, 987
VHDL
     and logic operations, 1173
Vibrations
     in auditory perception, 585
     in musical instruments, 1079
     nested of physical systems, 1081
Video
     radio signals associated with, 1188
Videogames
     use of randomness in, 1192
Vietnam war
     draft lottery in, 969
Vigenčre, Blaise de (France, 1523-1596)
     and ciphers, 1085
Vigenčre cipher, 599, 1085, 1086
Viking spacecraft, 1179
Villi (biology)
     formation of, 418
Vinogradov, Ivan M. (Russia, 1891-1983)
     and Goldbach's Conjecture, 911
Viroids, 1179
Virtual particles
     as basic quantum effect, 1059
     in Feynman diagrams, 1060
     and masses of particles, 1046
     and persistent structures, 540
     surrounding any particle, 1044
     and vacuum fluctuations, 1062
Viruses
     as fairly optimal organisms, 398
     genetic programs of, 1002
     self-assembly in, 1193
     shapes of, 385
Viruses (computer), 1179, 1182
Viscosity
     in 2D fluids, 999
     effects of in fluids, 381, 996
     and higher-order Lorenz equations, 998
     in models of turbulence, 997
     in quantum field theory, 1061
Visible lattice points, 613, 1093
Visual acuity, 1076
Visual cortex, 580, 1075
Visual illusions, 1076
Visual memory, 623
Visual perception, 577-584
     assessing models with, 365
     and color in this book, 851
     in computer experiments, 111
     difficulty of analyzing radio signals with, 1189
     eye movements in, 1192
     history of studies on, 1076
     implementation in brain, 1075
     and ocular dominance stripes, 1013
     and Stone Age paintings, 839
     and styles of art, 872
     and zebra as camouflaged, 1012
Visual presentation
     and inadequacy of language, 631
Visual thinking
     in mathematics, 1177
Vitamin A
     in embryo development, 1009
VLF radio receiver, 1187
VLSI
     Boolean formulas and, 1097
     testing and randomized algorithms, 1085
Vocal tracts
     and bird songs, 826
     and sound compression, 1080
Vocoders, 1080
Voices
     random variations in, 1192
Void
     and Epicurean notion of space, 1028
Volatility
     of prices in markets, 1015
Volcanos
     circular shapes of, 1187
     as landscape elements, 1001
Voltage
     and gauge invariance, 1045
Volumes
     and metrics, 1050
     of spheres in curved space, 1050
Volute shells
     patterns on, 423
von Kármán, Theodore (Hungary/Germany/USA, 1881-1963)
     and vortex streets, 998
von Koch, N. F. Helge (Sweden, 1870-1924)
     and nested curves, 934
von Neumann, John (Hungary/USA, 1903-1957)
     and CAs, 876, 879, 928
     and computers, 1108
     and history of complexity, 862
     and iterated maps, 919
     and random generators, 975
     and self-reproduction, 1179
     and set theory, 1154
     and thermodynamics of computation, 1020
     and universal CAs, 1117
     and use of universality, 1110
von Neumann-Bernays-Gödel set theory , 1155
von Neumann neighborhood (in 2D cellular automata) , 170, 928
von Neumann's Law
     for random networks, 1039
Voronin, Sergei M. (Russia, 1946- )
     and zeta function universality, 918
Voronoi diagrams, 987
     discrete, 987
     and nearest-neighbor memories, 1101
     and polycrystalline materials, 993
     and random networks, 1038
     in sphere packing, 986
Voronoi region
     and CA lattices, 929
Vortex atoms
     in the ether, 1044
Vortex streets, 377, 998
Vortices
     of Descartes, 1027
     in flow of sand, 1001
     in fluid flow, 376
     and general study of form, 967
     interactions between, 382, 998
     as localized structures, 990
     as topological defects, 1045
Vorticity-based models, 999
Vorticity patterns in fluids, 997
Vowels
     sound of, 1079
     and soundex system, 1100
Voyager spacecraft, 1190