# Index

K^{0} particle

and time reversal violation, 1019

K_{3,3} non-planar graph, 527

Kabala (universal object), 1127

Kaluza, Theodor F. E. (Germany, 1885–1954)

and notions of space, 1028

Kampé de Fériet hypergeometric functions, 1009

Kaneko, Kunihiko (Japan, 1956– )

and continuous CAs, 922

in Preface, xiii

Kansas

grid of towns in, 1187

Kant, Immanuel (Germany, 1724–1804)

and complexity in biology, 861

and free will, 1135

and purposes in nature, 1185

Karatsuba, Anatolii A. (Russia, 1937–[2008])

and multiplication, 1142

Kardar–Parisi–Zhang (KPZ) equation, 925

Kari, Jarkko J. (Finland/USA, 1964– )

and undecidability in 2D cellular automata, 1138

Kármán, Theodore von (Hungary/Germany/USA, 1881–1963)

and vortex streets, 998

Karnaugh maps, 1097

Kasiski, Friedrich W. (Poland, 1805–1881)

and cryptanalysis, 1086

Kauffman, Stuart A. (USA, 1939– )

and Boolean networks, 936

in Preface, xiii

Kazakhstan

straight railroad in, 1187

KdV equation

as exactly soluble, 1133

Kells

Book of, 873

Kelvin (William Thomson) (Scotland, 1824–1907)

and harmonic analyzer, 1107

and minimum area packings, 988

and models of space, 1027

and Monte Carlo methods, 1192

and thermodynamics, 1019

and vortices in ether, 1044

Kelvin–Helmholtz instabilities, 988

Kepler, Johannes (Germany, 1571–1630)

and 2-body problem, 972

and computers, 1107

and Fibonacci numbers, 891

and inhabitants of Moon, 1190

and rules of nature, 860

and snowflakes, 992

and sphere packings, 986

Keratin

repetitive structure of, 1003

Kernels

in visual perception, 579

Kerr solution

as exact solution, 1133

and time and computation, 1130

Key sequences

in cryptography, 598

Keyboard characters

for programs in notes, 854

Keystrokes

number to create this book, xiv

as source of randomness, 970

`Khinchin`

(Khinchin's constant), 914

Kidney ducts

branching in, 1008

Kinetic theory

and diffusion equation, 1024

and thermodynamics, 1019

"Kingdom was lost"

and chaos theory, 971

Kingdoms of organisms, 1003

Kingsnake

pigmentation pattern of, 426

Kirby, Laurence A. S. (England/USA, 1952– )

and unprovable statements, 1163

Kirkpatrick, E. Scott (USA, 1941– )

in Preface, xiii

and simulated annealing, 985

Kites

characteristic shapes of, 1183

Kleene star (`RepeatedNull`

), 957

Klein, Oskar (Sweden/Denmark/USA, 1894–1977)

and notions of space, 1028

Klein–Gordon equation

discretization of, 1060

vs. sine-Gordon, 922

Kleinian groups

and circle packings, 986

`KleinInvariantJ`

(modular elliptic function)

and almost integers, 915

Knapping (of stone tools), 1183

Kneading

randomness in, 306

Kneading sequences, 955

Knossos

maze at, 873

Knots

Alexander moves in, 1038

as complex artifacts, 1183

as constructed by rules, 875

in ether as atoms, 1028, 1044

model of atoms as, 1024

as not in 1D systems, 927

theory of, 1046

Knuth, Donald E. (USA, 1938– )

and dragon curves, 893

and Knuth–Bendix procedure, 1037

in Preface, xiii

and tests of randomness, 1084

Knuth–Bendix procedure, 1037

Koch, N. F. Helge von (Sweden, 1870–1924)

and nested curves, 934

Koch curve, 191, 933

history of, 934

Kolakoski, William G. (USA, 1944–1997)

and cyclic tag systems, 895

Kollectiv (collective)

and defining randomness, 1068

Kolmogorov, Andrei N. (Russia, 1903–1987)

and algorithmic randomness, 1068

and fluid turbulence, 997

Kolmogorov complexity

see Algorithmic information

Kondo model, 1057

Koran

calligraphy from the, 874

Korec, Ivan (Slovakia, 1943–1998)

and encodings of arithmetic, 1163

and register machines, 1121

KPZ (Kardar–Parisi–Zhang) equation, 925

Krohn–Rhodes decompositions, 1069

Kronecker product, 1073

`KroneckerDelta`

and orthogonal bases, 1072

Kufi calligraphy, 874

Kummer, Ernst E. (Germany, 1810–1893)

and Fermat's Last Theorem, 1166

Kuramoto–Sivashinsky equation, 925

Kuratowski's theorem, 1045

Kurdyumov, Georgii L. (Russia, 1953– )

and transitions in CAs, 981