W particle, 1046

Waddington, Conrad H. (England/Scotland, 1905–1975)
and patterns on shells, 1012

Wagner's theorem, 1045

Wainwright, Thomas E. (USA, 1927–[2007])
and molecular dynamics, 879, 999

Wajsberg, Mordechaj (Poland, 1902 – ~1940)
and axioms for logic, 1151

Wakes in fluid flow, 376, 984, 998

Waldmeister (automated theorem prover), 1158, 1174
lengths of proofs from, 1175

Walker, Crayton C. (USA, 1932– )
and Boolean networks, 936

Walking
fluid flow when, 996
as repetitive process, 1011

Walks, random
see Random walks

Wallpaper
and 2D cellular automata, 929

Walras, M. E. Léon (France, 1834–1910)
and math economics, 1015

Walsh, Joseph L. (USA, 1895–1973)
and Walsh transforms, 1073

Walsh transforms, 573, 1072
fast, 1073

Wang, Hao (China/USA, 1921–1995)
and lag systems, 894
and tag systems, 1120
and undecidability in tiling, 1139

"Want of a nail..."
and chaos theory, 971

Waring, Edward (England, 1736–1798)
and Waring's Problem, 910

Waring's Problem, 910
as unsolved problem, 1166

Warp drive
determining possibility of, 1027
and extraterrestrial contact, 1190

Wasp nests
as animal artifacts, 1184
form of, 385

Watchmaker
and argument by design, 861

Water
boiling of as discrete transition, 337
and definition of life, 825
and extraterrestrial life, 1179
flow patterns of, 376
and landscape structure, 1001
stream breaking into drops, 984
viscosity of, 996

Water hole (SETI frequency band), 1189

Watersheds
in memory landscape, 1101
and Voronoi diagrams, 987

Wave equation, 163
higher-dimensional, 923
as hyperbolic equation, 940
origin of, 923
transformation of time in, 732

Wave packet
collapse of the, 1063

Wave-particle duality, 1056
as basic quantum effect, 1058
and discrete space, 1027
and elementary particles, 1044

Wave theory of light, 1041

Waveforms
curves of, 146
in FM synthesis, 1079
for sound, 585

Wavelength distribution
in color vision, 1074

Wavelets, 1074
and substitution systems, 893
and texture generation, 1077

Waves
in fracture processes, 995
on ocean surfaces, 304, 1001
in quantum field theories, 1061
in quantum theory, 1056
and repetitive behavior, 355
superpositions of, 984
as yielding discreteness, 984

Wax impressions, 1178

Weaire, Denis L. (Ireland, 1942– )
and minimum area packings, 988
in Preface, xiii

Weak interactions (in particle physics), 1025, 1057

Wear
in stone tools, 1184

Weather, 1177
and bifurcations, 972
and forms of snowflakes, 992
as having a mind of its own, 822
maps, 1178
prediction and computational irreducibility, 1132
satellite images from, 1187

Weaving
as origin of ornament, 872
patterns for from CAs, 872
programming of patterns for, 1107
rules in, 874

Web
and amateur science, 1180
randomness in transactions on, 1192

Weber's law, 1014

Webs (spider)
as animal artifacts, 1184
patterns in, 1011

Website
list of questions on, 856
and programs in the notes, 854
for this book, iv, 849

Weibull distribution, 977

Weierstrass, Karl T. W. (Germany, 1815–1897)
and nested curves, 918, 934

Weierstrass functions, 918
and 1/f noise, 969

WeierstrassP (Weierstrass function)
in solution of spinning top, 1133

Weighted cellular automata
implementation of, 1012

Weighted random sequences, 976

Weights
in additive cellular automata, 952
of connections to nerve cells, 1075
of forms in image compression, 574
in neural networks, 1102

Weights of humans
distribution of, 977, 1003

Weinberg–Salam model, 1025

Weizsäcker, Carl F. v. (Germany, 1912–[2007])
and discreteness of space, 1027

Welch, Terry A. (USA, 1939–1988)
and data compression, 1069

Well-formed formulas
in predicate logic, 1150
and truth values, 1158

Wells, Herbert G. (England, 1866–1946)
and time travel, 1031

Westminster Abbey
decoration in, 873

Weyl, Hermann K. H. (Germany/Switzerland/USA, 1885–1955)
and gauge invariance, 1045
and gauge theories of space, 1028

Weyl tensor, 1049

WFFs (well-formed formulas)
in predicate logic, 1150
and truth values, 1158

Whale songs, 826, 1180

Wheeler, John A. (USA, 1911–[2008])
and discreteness of space, 1027
and geons, 1054

Wheels
characteristic shapes of, 1183

Wheels of fortune, 306

While (loop)
and decimation systems, 909
and pointer-based encoding, 1071
and Pollard rho factoring, 1090
and rule 110 proof, 1116
see also NestWhile

Whimsical descriptions, 850

Whisk ferns, 1004

Whistlers (radio signals), 1187
in early SETI, 1188

White noise
origins of, 969, 988

Whitehead, Alfred N. (England/USA, 1861–1947)
and axioms for logic, 1151
and foundations of math, 1149
and math in science, 859
and Principia Mathematica, 894
and universal algebra, 1150

Whitney embedding theorem, 1045

Whorf, Benjamin L. (USA, 1897–1941)
and language and thinking, 1181

Whorls
number of in shells, 1008

Wick rotation (in quantum field theory), 1043, 1061

Wiener, Harry (USA, 1924–1998)
and alkane boiling points, 1195

Wiener, Norbert (USA, 1894–1964)
and history of complexity, 862
and reaction-diffusion, 1013

Wiesenfeld, Kurt A. (USA, 1958– )
and self-organized criticality, 989

Wigner–Seitz cells
and CA lattices, 929
and Voronoi diagrams, 987

Wigner's semicircle law, 977

Wiles, Andrew J. (England/USA, 1953– )
and Fermat's Last Theorem, 1166

Will
origins of free, 750
and purpose, 1136
see also Free will

Willow leaves, 1006

Wilson loops (in QCD), 1062

Wind
and desert landscapes, 1001
and ocean surfaces, 1001
patterns produced by, 1183
recognizing motion from, 1183
turbulence and gusting in, 1001

Wind chimes, 827

Wind-tree models (dynamic lattice gases), 999

Winding number, 1045

Windows (operating system)
and creation of this book, 854

Winfree, Arthur T. (USA, 1942-[2002])
and reaction-diffusion, 1013

Winner-takes-all cellular automata, 339

Wire chambers (particle detectors), 969

Wire rope
and nested patterns, 874

WireWorld cellular automaton, 1117

Wisdom, Jack L. (USA, 1953– )
and chaos in solar system, 973
in Preface, xiii

Witten, Thomas A., Jr. (USA, 1944– )
and diffusion-limited aggregation, 994

Wittgenstein, Ludwig J. J. (Austria/England, 1889–1951)
and philosophy of language, 1181
and truth tables, 1170

Wolfram Research, Inc.
and creation of this book, xii
and history of this book, 20
and my personal timeline, 864
as producers of Mathematica, 853

Wolpert, Lewis (England, 1929– )
and embryology, 1010
in Preface, xiii

Word chains (evaluation chains), 1095

Word equations (sequence equations), 944, 1141

Word frequencies
and Zipf's law, 1014

Word problems, 1141
and manifold equivalence, 1051
for semigroups and undecidability, 1136
undecidability in, 1138
and use of set theory, 1160

Word-processing software, 1108

Words
cube-free (and Thue–Morse sequence), 890
hashing of, 1100
number of in languages, 1103

Works of God
natural forms as, 872

World models
and systems theory, 862

World War II
cryptography after, 1085

Worm
Paterson's, 930
self-reproducing computer, 1179

Worm shell
growth of, 415

Worship
and animism, 1195

Worthington, Arthur M. (England, 1852–1916), 1000

Wozniakowski (digit reversal) sequences, 905

Wraparound system, 255

Wren, Christopher (England, 1632–1723)
and shapes of shells, 1008

Wrinkling, 996

Writing
development of, 1184

Writing style
of this book, 849

Wulff shapes
in CA growth, 929
and CA lattices, 929