C60
and spherical networks, 1049
Cabala (universal object), 1127
Cabbage
phyllotaxis in, 409
Cable (wire rope)
and nesting in, 874
Cactus
phyllotaxis in, 409
regular shape of, 385
CAD (cylindrical algebraic decomposition), 1154
Caesar, Julius (Italy, 100-44 BC)
and cryptography, 1085
Caesar ciphers, 1085
Cages (small girth networks), 1029
Cahn-Hilliard equation, 980
Calabi-Yau manifolds, 1028, 1052
Calcite
hopper crystals in, 993
Calculators
chaos experiments on, 919
and history of computing, 1107
reverse Polish notation in, 896
Calculus
axioms for, 774
and computational reducibility, 1132
and continuous computation, 1129
equations based on, 161
history of notation for, 1182
and natural selection, 394
origin of word, 925
proofs in, 1177
role in history of science, 44
see also Propositional logic
Calculus of variations
and geodesics, 1049
Calculus ratiocinator
of Leibniz, 1149
California Institute of Technology, xiii
Calligraphy
Kufi, 874
Calls
of birds, 1180
Calogero-Moser model, 1133
Camouflage
stripes of zebras as, 1012
use of randomness in, 1192
and visual perception, 1077
Campbell, John H. (USA, 1938- )
and patterns on shells, 1012
in Preface, xiii
Cams
characteristic shapes of, 1183
for randomness generation, 969
Canalizing behavior (class 2 Boolean networks), 936
Canals
on Earth and Mars, 1180
Cancers
from DNA errors, 970
see also Tumor growth
Cannon balls
packing of, 986
Canonical ensemble
in 2D Ising model, 982
and path integrals, 1061
Canonical forms
establishing axioms with, 1170
in multiway systems, 1036
in proof searching, 1157
and proofs in logic, 1175
see also Confluence
Canonical quantization, 1057
of gravity, 1054
Canonical systems
see Multiway systems
Canons
rules for musical, 875
Cantor, Georg F. L. P. (Germany, 1845-1918)
and Cantor set, 893
and the continuum, 1127
and definition of dimension, 1030
and diagonal arguments, 1128
and digit sequences, 902
and history of numbers, 901
and real numbers, 1153
and set theory, 1154
and transfinite numbers, 1162
Cantor normal form
and Goodstein sequences, 1163
for ordinal numbers, 1162
Cantor pairing function (sigma), 1127
Cantor set
attractors as forming, 959
and CA cardinality, 1128
and CA state space, 869, 958
from continuous systems, 1130
generating function for, 1092
properties of, 890
Sarkovskii's theorem for, 955
and shift registers, 975
spectrum of, 586, 1081
from substitution system, 83
Cantor's diagonal argument, 1127
Capacity (dimension), 959
Capillaries
branching in, 413, 1008
Capital Asset Pricing Model (CAPM), 1015
Caps on sphere
areas of, 1050
Carbon dioxide
and life on Mars, 1180
Cardinality
and the continuum, 1127
Cardinals
as generalizing numbers, 1168
as transfinite numbers, 1162
Cards
shuffling of, 968, 974
for storing programs, 1107
CarmichaelLambda
and linear congruential periods, 974
and quadratic generators, 975
Carnot, Sadi N. L. (France, 1796-1832)
and thermodynamics, 1019
Carpets
and 2D cellular automata, 929
Sierpinski, 188
Carrier frequencies, 835, 1188
Carrot leaves, 385, 1006
Carry digits
in arithmetic, 124
non-locality of, 730
in powers, 1093, 1112
in subtraction, 870
and Turing machines, 760
Cars
engine knocking in, 1194
evolution in, 1003
as randomness analogy, 304
traffic models, 1014
turning tracks of, 418
|  | Cartesianism
and matter in space, 1028
see also Descartes, René
Cartilage
as precursor of bone, 1010
Cartoons
and visual perception, 1076
Cartwright, Mary L. (England, 1900-1998)
and chaos theory, 971
CAs
see Cellular automata
Cascades of eddies, 997
Casimir, Hendrik B. G. (Netherlands, 1909-2000)
and electron model, 1044
Casimir effect, 1062
and uniform spectra, 988
Casinos
and randomness of dice, 969
Castel del Monte
and nested architectural forms, 874
Catalan, Eugène C. (Belgium, 1814-1894)
and iterated aliquot sums, 911
Catalan (Catalan's constant)
and dimer problem, 959
from rational integral, 916
Catalan numbers (Binomial)
and balanced parentheses, 989
and Cantor set, 890
and number of expressions, 897
Catalan's Conjecture, 1166
Catalysis
repeatable randomness in, 976
Catalysts
searching for, 1193
Catastrophe theory
and biological form, 1004
and curved surfaces, 1009
discreteness from, 984
in rate equations, 984
summary of relations to, 12
Catch
and context-free parsing, 1103
and pointer-based encoding, 1071
and testing invariances, 1022
and testing reversibility, 1017
Categoricity
of axiom systems, 799, 1172, 1172'
Category theory
axioms for, 774
history of, 1154
and idealization of math, 1150
and spin networks, 1055
Catenary
characteristic shape of, 1183
as exactly soluble, 1133
Caterpillars
eating paths of, 1011
Catfish
pigmentation pattern of, 426
Cats
patterns in tortoiseshell, 1014
Cauchy functional equation, 953
Cauchy problem
vs. constraints, 940
for general relativity, 1053
Cauchy surfaces, 1041
Cauliflower shape, 385
Causal invariance, 503
and concept of motion, 522, 529
and distributed computing, 1035
and emulated CAs, 1035
and gauge invariance, 527
for networks, 515
and quantum phenomena, 542
in simulating mobile automata, 1034
Causal networks
and cosmology, 1056
curvature in, 534
difficulty of deducing, 493
as directed graphs, 1033
from evolution history, 1033
exponential growth in, 496
and general relativity, 1053
as Hasse diagrams, 1033
history of, 1032
implementation of, 1033
and information transmission, 520
invariance of, 503
loops in, 494
from mobile automata, 488, 1033
from multiway systems, 507
vs. multiway systems, 1037
in network evolution, 514
and perceived spacetime, 516
and posets, 1040
random, 1052
and replacement orders, 501
reversibility in, 495
slices through, 516
from substitution systems, 497
and torsion, 1052
Causality
and Bell's inequalities, 1065
and free will, 1136
Causes
compared to regularities, 352
Caustics
and classical limits, 1059
discreteness from, 984
Cave paintings
interpretation of, 839
purposes of, 1184
recognition of, 874
and visual perception, 1076
Cayley, Arthur (England, 1821-1895)
and group theory, 1153
and iterated maps, 918
Cayley graphs, 938
cellular automata on, 930
and hyperbolic space, 1050
limiting geometry of, 1051
and network constraints, 1032
and sorting networks, 1142
Cayley's theorem
as example theorem, 1159
CCITT compression standard, 1070
CCSR (Center for Complex Systems Research), xiii
CDC 7600 computer, 854
CDMA
and radio signals, 1188
and SETI, 1190
and shift registers, 1086
CDs (compact discs)
bandwidth of, 1079
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