# Index

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

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