Index



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

Vigenère, Blaise de (France, 1523-1596)
and ciphers, 1085

Vigenère 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