# 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 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 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