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–[2010])
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 π, 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 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–[1997])
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
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