Gibbs, J. Willard (USA, 1839-1903)
and statistical mechanics, 1020
Gibbs phenomenon, 917
and experimental math, 899
and image compression, 1074
Gibbs-Thomson effect, 993
GIF compression, 1070
Gila monster
pigmentation pattern of, 426
Gilbreth, Frank B. (USA, 1868-1924)
and causal networks, 1033
Gilbreth, Lillian E. M. (USA, 1878-1972)
and causal networks, 1033
Gilgamesh, Epic of, 873
Ginger leaves, 1006
Giraffe
pigmentation pattern of, 426
Girth
of networks, 1029
Glaisher, James W. L. (England, 1848-1928)
and binomials mod k, 870
Glare filters (polarizers), 1064
Glass (material)
as amorphous material, 994
fracture in, 994
Gleick, James W. (USA, 1954- )
and chaos theory, 972
Glider gun
in code 1329, 288
in Game of Life, 965
in rule 110, 293, 964
Gliders, 284
in continuous CAs, 160
and emulation of Nand, 1117
in Game of Life, 249, 964
in rule 110, 292, 964
see also Localized structures
Global minima, 347
Global Positioning System
see GPS
Globular clusters
and thermodynamics, 1021
Glueballs (in QCD), 1061
Gluons (in QCD), 1057
confinement of, 1061
Glycerine
viscosity of, 996
Gnomons
and Euclid's algorithm, 915
and forms of growth, 1008
and substitution systems, 932
Go, game of, 875
Goats
fortune-telling from, 968
God
and character of space, 1028
and complexity, 861
and free will, 1135
identified with universe, 1196
and objects in nature, 828
and origin of complexity, 3
and phenomena in astronomy, 834
and physics as intelligence, 1191
and purpose for universe, 1185
as source of complexity in biology, 1001
and ultimate theory of physics, 1025
and universe as intelligent, 1196
see also Religion
see also Theology
Gödel, Kurt F. (Austria/USA, 1906-1978)
and character of math, 1176
and consistency of arithmetic, 1168
and defining computability, 1126
and experiment in math, 899
and Gödel's Theorem, 879, 1158
and origins of universality, 1110
and predicate logic, 1152
and register machines, 896
and undecidability, 1136
Gödel beta function, 1121
and primitive recursion, 908
Gödel numbers
and encoding lists, 1120
and history of universality, 1110
Gödel's Completeness Theorem, 1152, 1167
for equational logic, 1172
Gödel's Theorem, 1158
and arithmetic systems, 673
and Church's Thesis, 1125
and determinism, 1132
and Diophantine equations, 1161
encoding of statements in, 785
encodings used in, 816
and free will, 1135
and history of math, 1149
and history of universality, 1110
as limitation on math, 7, 1135
practical relevance of, 791
as precursor to my work, 879
proof of using rule 110, 786
and truth, 1167
and universality of arithmetic, 784, 1152
and unprovable statements, 782
use of recursive functions in, 907
Gods
animism and, 1195
as source of randomness, 967
Goethe, Johann W. v. (Germany, 1749-1832)
and morphology, 1004
Golay, Marcel J. E. (USA, 1902-1989)
and error-correcting codes, 1101
and hexagonal CAs, 928
Golay codes
and sphere packings, 987
Golay neighborhood (hexagonal cellular automata), 928
Gold
hopper crystals in, 993
Goldbach, Christian (Russia, 1690-1764)
and polynomials for primes, 909
Goldbach's Conjecture, 135, 911
stated in Peano arithmetic, 1162
true if unprovable, 1167
as unsolved problem, 1166
GoldenRatio
and 2D substitution systems, 932
and entropy in rule 32, 958
and Fibonacci encoding, 1070
and general study of form, 967
and growth rate of multiway system, 205
and Penrose tilings, 932
as Pisot number, 903
and plant phyllotaxis, 408, 1006
properties of, 890
and running time of Euclid's algorithm, 1147
and spectra, 1081
Golf balls
and circle packings, 985
Golomb, Solomon W. (USA, 1932- )
and nonlinear shift registers, 878
and polyominoes, 943
in Preface, xiii
and shift registers, 879, 1088
Goodstein, Reuben L. (England, 1912-1985)
and Goodstein sequences, 1163
Goodstein sequences
proofs about in set theory, 1160
and unprovability, 1163
Goosefoot leaves, 1006
Gosper, R. William (USA, 1943- )
and dragon curves, 893
and experimental math, 899
and Game of Life, 965
in Preface, xiii
Gothic windows
nesting in, 873, 874
Government control
and computational irreducibility, 1132
Government regulation
of games of chance, 1084
GPS (Global Positioning System)
and SETI, 1190
and shift registers, 1086
and time dilation, 524, 1042
Gradient descent
implementation of, 985
in neural networks, 1102
for satisfying constraints, 344
Gradualism
in biological evolution, 395
Grain patterns
and repeatable randomness, 976
Grains (in solids)
evolution of, 1039
and Voronoi diagrams, 987
Grammar-checking software, 1104
Grammars
and concept of programs, 860
context-free, 939, 1103
context-sensitive, 939
of formal languages, 938
of human languages, 630, 1103, 1181
of math expressions, 1150
of ornament, 872
random, 1084
and redundancy, 1086
regular, 939
as systems based on rules, 875
and Turing machines, 961
two-dimensional, 1104
unrestricted, 939
|  | Grand unified models (in physics), 1025, 1043
Granular materials
flow in, 1001
packing in, 986
Grape leaves, 401, 1006
Graph-based systems, 193-203
Graph grammars, 1040
Graph isomorphism
and NP completeness, 1146
Graph layout, 193
Graph theory
and discrete packings, 987
and planarity of networks, 1045
Graphical interfaces, 1102
Graphical representation of time, 1031
Graphical user interfaces
as alternative to language, 631
and history of computing, 1108
Graphics
as basis for analysis, 111
production of in this book, 851
Graphics3D
and 3D cellular automata, 927
Graphs
for attractors, 277
cellular automata on, 930, 936
small, 194
see also Networks
Grass
growth of, 1004
and Kant on complexity, 861
Grassmann, Hermann G. (Germany, 1809-1877)
and axioms for arithmetic, 1152
Grassmann algebra
as generalizing numbers, 1168
Gravitational waves
detectors of, 1048
and speed of light, 1041
in vacuum, 536, 1053
Gravitons, 1054
as particles, 1043
and space vs. matter, 1028
Gravity, 530-537
CPT violation in, 1019
in early universe, 1021
history of, 1047
n-body systems subject to, 1021
particle production by, 1062
randomness in systems under, 313
and time and computation, 1130
in ultimate theory of physics, 469
and vacuum fluctuations, 1062
Gray, Alfred (USA, 1939-1998)
and parametric curves, 1009
in Preface, xiii
Gray code, 901
and concatenation sequences, 913
and constraint satisfaction, 984
and math functions, 731
as ordering of CAs, 352, 885
and ordering of Walsh functions, 1073
Gray levels
dithering to get, 1077
Great Chain of Being, 1197
Great circles
as geodesics, 1049, 1050
Great Mosque of Córdoba, 873
Great Pyramid, 874
Great Wall of China, 1187
Greek art, 43, 873
Greek biology, 1003
Greek embryology, 1010
Greek grammars, 875
Greek mathematics
and labelling in geometry, 1182
and proof, 1149
rules in, 875
Greek mineralogy, 993
Greek number system, 1182
Greek philosophy
and atomism, 876
and complexity, 861
and definition of life, 1178
and extraterrestrial life, 1180
and free will, 1135
and math in science, 859
and universality, 1109
Greek physics
and ultimate theories, 1024
Green, Milton W. (USA, 1926- )
and sorting networks, 1142
Greenberg, James M. (USA, 1940- )
and reaction-diffusion, 1013
Green's functions
for additive systems, 952
for cellular automata, 950
grep
and regular expressions, 958
Grids
cellular automata on, 169
lines at slopes on, 916
superimposing, 613, 1078
visible from space, 1187
Grigorchuk, Rostislav I. (Ukraine/Russia, 1953- )
and intermediate growth groups, 938
GroebnerBasis
and completion algorithms, 1037
and NP completeness, 1143
Gromov, Mikhael L. (Russia/France/USA, 1943- )
in Preface, xiii
and random groups, 938
Ground state
of quantum field theories, 1062
of spin systems, 944
Groupoids, 1171
Groups (mathematical), 1153
and abstraction in math, 792
axioms for, 773
axioms for finite, 1176
and CA conservation laws, 1023
CAs based on, 887, 956
Cayley graphs of, 1032
commutative
see Commutative groups
constraints defining, 945
decidability with commutativity, 1159
emulating Peano arithmetic, 1159
enumeration of, 805
and forcing by axioms, 1172
and gauge theories, 1045
from generators and relations, 1169
inessential incompleteness of, 800
limiting geometry of, 1051
and multiway systems, 938
number of, 945
and operators allowed by axioms, 1172
and particles in physics, 528
PCP and undecidability in, 1139
polyadic, 1171
random, 938
shortest axioms for, 806
and sphere packings, 986
symmetry for lattices, 980
theorems in pure theory of, 1159
undecidability of equivalence of, 1138
universality of, 784, 1159
word problem for, 1141
Growth
as amplifying randomness, 970
of animals, 413-422
of crystals, 369-373
of cyclic tag systems, 96
Eden model for, 331, 978
general constraints on, 1010
general schemes for, 1011
history of studies in biology, 1003
and maintaining flatness, 1007
parametrizations of, 1010
of plants, 400-413
of sheets of tissue, 412
undecidability of continued, 1138
Growth and Form (book), 1004
Growth inhibition
in plant phyllotaxis, 409
in snowflake growth, 370
Growth rates
in computational complexity theory, 1143
and curvature in networks, 533
general theory of, 1162
in multiway systems, 205, 937
and network dimensions, 478, 1030
of number of trivalent networks, 1029
in recursive functions, 908
in substitution systems, 890
in symbolic systems, 897
in Turing machines, 761, 1145
see also Differential growth
Growth rules
for 1D cellular automata, 24
for 2D cellular automata, 928
Growth totalistic rules, 928
Grzegorczyk hierarchy, 906
GUIs (graphical user interfaces), 1103
and history of computing, 1108
Gullies (in landscapes), 1001
Gustatory (taste) sense, 1105
Gusting of wind, 1001
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