Crackling
in natural radio emissions, 1187

Cracks
nesting of, 988
randomness of, 374

Craters
circular shapes of, 1187
as landscape elements, 1001

Creation myths
as models, 992

Creeping flow, 377

Crete
maze at Knossos on, 873

Criminal law
free will in, 1135

Crinkling
patterns of, 996

Critical exponent
in 2D Ising model, 982

Critical pairs
in completion algorithms, 1037

Critical phenomena
and nesting, 989
and phase transitions, 981
and scale invariance, 955

Crossovers
in genetics, 970

Crosstalk
and Walsh functions, 1073

Crowds
motion of people in, 1014

Crumpling
patterns of, 996

Crushing (of solids), 995
nesting in, 988
and sphere packing, 986

Crust (of Earth)
and origin of life, 1179
patterns on, 1001

Crutchfield, James P. (USA, 1955– )
and Markov models, 1084
in Preface, xiii

Cryptanalysis
of additive cellular automata, 601
and dead languages, 1185
and defining randomness, 1068
history of, 1086
and history of computing, 1107
of linear congruential generators, 1089
and meaning of programs, 1183
and rule 30 NP completeness, 770
of shift registers, 1087
of Vigenère ciphers, 599

Cryptography, 598–606
as application of randomness, 1192
and defining randomness, 1068
with digit sequences, 1089
electronic randomness for, 968
as example of technology, 840
and hashing, 1100
history of, 1085
and history of complexity, 49
as process based on rules, 875
quantum, 1058
random keys for, 970
and recognizing meaning, 827
and shift registers, 878, 1086

Crystal growth, 369–373
history of, 993
models of, 993

Crystal lattices
systems on, 169, 929

Crystals
as artificial-looking, 828
Brillouin zones in, 988
diffraction patterns in, 1082
effect of seeds on, 992
formation as phase transition, 983
fracture in, 374
hopper, 993
lack of continuum limit for, 327
as not artifacts, 1183
randomness in shapes of, 373
as self-organizing systems, 824
shapes of, 929
trivalent network and, 1030

Csc (cosecant)
and Moire patterns, 1078

Cube-free sequences, 944
Thue–Morse and, 890

Cube network, 476
transformed to tetrahedron, 1038

Cube roots
and Cantor set generating function, 1092
digits of, 141

Cubes
equations involving sums of, 945
produced by CAs, 1186

Cubic equations
and computational reducibility, 1132
Diophantine, 1164
as exactly soluble, 1133
iterative solutions to, 1101
size of solutions to, 945

Cubic graphs
see Networks, trivalent

Cubic lattices
cellular automata on, 182
class 4 rules on, 949
as crystal lattices, 929
random walks on, 977
Voronoi diagrams for, 987

Cuboid
and 3D cellular automata, 927

Cucumber leaves, 1006

Cultural relativism
not connected to relativity, 1042

Culture
and character of perception, 635
and defining intelligence, 1178
and recognizing intelligence, 825
and response to events, 827

Curie point
in Ising model, 981

Curl
and vector potential, 1045

Curry, Haskell B. (USA, 1900–1982)
and combinators, 898

Currying
and combinators, 1122
of function arguments, 896

Curvature
of curves, 1049
curves defined by, 418, 1009
in differential geometry, 1048
of fronts in crystal growth, 993
gauge fields as, 1045
of growing tissue, 1007
higher-dimensional, 1009
in non-integer dimensions, 1051
in plant growth, 412
in rivers, 1001
singularities in, 1053

Curves
curvature of, 1049
Lissajous, 917
mathematical, 145–148
space-filling, 893

Cusps
in light caustics, 984

Custering
in 2D cellular automata, 877

Cut elimination in proofs, 1155

Cuttlefish
communication by, 1181
pigmentation pattern of, 426

Cybernetics
and biology, 1004
and computational irreducibility, 1132
and definition of complexity, 1068
and free will for machines, 1135
history of, 862
and models of thinking, 1099
as precursor to my work, 879
and self-reproduction, 1179
summary of relations to, 14

Cycles
in attractors, 958
longest in networks, 1029, 1031
in random networks, 963
and repetition periods, 950
in shift rules, 963
shortest in networks, 1029
in state transition graphs, 961

Cyclic
see Repetitive

Cyclic addition systems, 255, 950
state transition graphs for, 961

Cyclic boundary conditions
in CA implementation, 866
periods in CAs with, 950

Cyclic groups
decomposition into, 1172

Cyclic multiplication, 257, 950
state transition graphs for, 961

Cyclic negation
in multivalued logic, 1175

Cyclic shift instructions, 951

Cyclic subgroups
and nested patterns, 956

Cyclic tag systems, 95
emulated by rule 110, 678
emulated by tag systems, 1113
emulating cellular automata, 668
emulating tag systems, 669, 1116
generalizations of, 895
implementation of, 895
mechanical version of, 895
and pointer-based encoding, 1071
random initial conditions in, 949
randomness generation in, 920
vs. shift registers, 1088

Cyclones (in weather), 1178

Cyclotomic (cyclotomic polynomials)
and shift register periods, 975
and solution of logistic map, 1098

Cylinders
in curved space, 1050
and definition of Ricci tensor, 534
fluid flow past, 996

Cylindrical algebraic decomposition, 1154

Cypress leaves, 1006