C (programming language)
and chaos experiments, 919
as example of language, 1109
and history of computing, 1108
and my first CA experiments, 864
my use of, 854, 899
programs for CAs, 865
and register machines, 101

C curve
from 1D substitution system, 892
from 2D substitution system, 190

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 (σ), 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
Sierpiński, 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

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