W particle, 1046
Waddington, Conrad H. (England/Scotland, 1905-1975)
and patterns on shells, 1012
Wagner's theorem, 1045
Wainwright, Thomas E. (USA, 1927- )
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- )
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- )
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
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