g (general intelligence factor), 1178

Gabor functions
in visual system, 1075

Gacs, Peter (USA, 1947– )
in Preface, xiii
and transitions in CAs, 981

Gaia Hypothesis, 1195

Galaxies
distribution of, 1021
and expansion of universe, 1055
formation of, 455, 1021
formation of and my work, 880
formation of and Voronoi diagrams, 987
patterns in, 835
and Second Law, 1021
and simple initial conditions, 1026

Galaxy
colonization of, 1191
radio emission in, 1188

Galena
hopper crystals in, 993

Galilean invariance
in cellular automata fluids, 999
in fundamental physics, 522
and relativity, 1042

Galilei, Galileo (Italy, 1564–1642)
and Galilean invariance, 1041
and math in science, 859
and models vs. reality, 991
and nature of gravity, 1047
and the nature of space, 1028
and theoretical biology, 1003

Galois, Evariste (France, 1811–1832)
and group theory, 1153
and quadratic continued fractions, 915

Galois fields, 1153
see also Finite fields

Galton board
randomness in, 312

Gambling
and defining randomness, 1068
and Gaussian distribution, 977
and randomness sources, 968

Game of Go, 875

Game of Life
and history of 2D CAs, 928
and history of CAs, 877
and history of complexity, 50
implementation of, 949
persistent structures in, 964
as precursor to my work, 880
random initial conditions in, 249
unbounded growth in, 965
universality in, 693, 1117

Game theory, 1104
and computational irreducibility, 1132
and laws in economics, 1014
and models of markets, 1015
and relation to cybernetics, 862

Games
and AI, 1099
between programs, 1105
and history of CAs, 877
and multiway systems, 939
randomness in, 968
rules in, 875

Games of chance
and defining randomness, 1067
and history of statistics, 1082
randomness in, 305, 968, 1192
and tests of randomness, 1084

Gaming regulations, 969

Gamma (gamma function)
argument structures for, 896
and curves from curvature, 1009
emulating If, 1129
from rational integrals, 916
as special function, 1092
and transcendental numbers, 912
see also Factorial

Gamma ray bursts, 1187

Gamuts
color, 1074

Gap test, 1085

Gaps
between primes, 133, 909

Garbage collection
in network systems, 199, 935

Garden of Eden
in cellular automata, 876, 961

Gardner, Martin (USA, 1914–[2010])
and Game of Life, 877

Gas clouds
as source of radio emissions, 1187

Gases
CA idealization of, 446
and chaos theory, 971
discrete models for, 999
extraterrestrials based on, 1180, 1190
flow of, 376
see also Fluid flow
as main application of Second Law, 451
thermodynamic theories of, 1019

Gasket
see Sierpiński pattern

Gastrulation (biological folding), 417, 1009

Gates
in practical computers, 1108
quantum, 1147
reversible logic, 1098
see also Boolean functions

Gauge bosons, 1043

Gauge invariance, 1045
and causal invariance, 527

Gauge theories
origin of, 1028
and quantum history, 1057

Gauss, J. Carl Friedrich (Germany, 1777–1855)
and Central Limit Theorem, 977
and curvature of surfaces, 1049
and Diophantine equations, 1164
and experimental math, 899
and extraterrestrials, 1189
and iterated maps, 919
and primes, 909
and sphere packings, 985, 986

Gauss circle problem, 910

Gauss map
and iterated maps, 919

Gaussian curvature
and biological growth, 1009
as invariant quantity, 1049

Gaussian distributions
as assumed in statistics, 1083
and Central Limit Theorem, 976
of constraint violations, 984
in laws of human behavior, 1014
vs. non-standard diffusion, 1024
not from self-avoiding walks, 978
as PDE initial conditions, 163
of price fluctuations, 1014
in quantitative traits, 1003
from random walks, 329
in visual system responses, 1075

Gaussian elimination
as iterative algorithm, 1141

Gauss's law
in cellular automata, 1023

GCD (greatest common divisor)
as associative function, 1094
and computational reducibility, 747
and correspondence systems, 1140
and cyclic addition periods, 950
encoded as integer equation, 1160
and Euclid's algorithm, 915
and FactorInteger, 1090
iterative algorithm for, 1141
and limited size periods, 257
pattern from, 613, 1093
and primitive recursion, 907
and sine curves, 917
sounds from, 1080

Gears
and computing devices, 1107

Geese
patterns in flocks of, 1011

Gegenbauer, Leopold B. (Austria, 1849–1903)
and GegenbauerC, 1091

GegenbauerC (Gegenbauer polynomials)
history of, 1091
and isotropy measures, 980
and rule 150 pattern, 612
and trinomial coefficients, 1091

Geiger counters, 969

Gels
in living systems, 1180

Gemstones
as faceted crystals, 370
synthetic, 993

Genealogical trees
as nested, 988
from substitution systems, 893, 1002

General intelligence factor, 1178

General-purpose computers
and history of universality, 1110
and universality, 642

General recursive functions, 907, 1121
and Church's Thesis, 1125

General relativity
and animal growth models, 1010
difficulty of solving, 1132
and gauge invariance, 1045
history of, 1048
need for explicit matter in, 537
as simple physical model, 1025
and space vs. contents, 1028
as theory of gravity, 530
and time and computation, 1130
and time travel, 1043
and ultimate theory of physics, 1025
variants of, 1048
with varying spacetime dimension, 1056

General systems theory
and history of complexity, 862
summary of relations to, 15

Generalization
in human thinking, 627
in mathematics, 792, 821, 1168

Generalization rule
in axioms, 1150

Generalized mobile automata, 76

Generating function
for additive cellular automata, 951
for balanced parentheses, 989
for cycles, 958
for DigitCount, 902
for Fibonacci, 890
modulo 2, 1092
for nested patterns, 1091
for regular languages, 957
for Thue–Morse sequence, 890
for Thue–Morse spectrum, 1081

Generative grammars, 938

Generators
in groups, 1141
and relations, 1169

Generic behavior
in chaos theory, 971

Genes
as analogs of functions in software, 1003
as components of genetic programs, 1002

Genetic algorithms, 1002
and combinatorial optimization, 985
for design optimization, 1193
and sequential substitution systems, 894

Genetic analysis
and multiway systems, 938

Genetic code
and theoretical biology, 1004

Genetic networks
and Boolean networks, 936

Genetic programming
and methods of prediction, 1105

Genetic programs
and cell positions, 1009
compared to laws of physics, 397
as foundation of biology, 383
and growth of animals, 419
and parts of animals, 417
searching for in biology, 842
smooth variations in, 394
structure of, 1002

Genetic sequences
matching of, 1101

Genetics
and definition of life, 1178
discrete features of, 1003
and mollusc shell patterns, 1012
randomness assumed in, 970
use of simple rules in, 860

Genomes
as programs, 383

Gentzen, Gerhard (Germany, 1909–1945)
and consistency of arithmetic, 1168
and transfinite induction, 1163

Genus
of algebraic surfaces, 1164
of networks, 1045

Geodesic balls
volumes of, 1050

Geodesic deviation
and Riemann tensor, 1049

Geodesic domes
characteristic shapes of, 1183
and curved space, 532
and spherical networks, 1049

Geodesics
and definition of dimension, 1031
distance defined by, 1048
divergence of and chaos, 971
in flat space, 1048
and paths of particles, 531
on surfaces, 1049

Geographic cycle (in landscapes), 1001

Geological fractures, 374, 995

Geometric mean
of continued fraction terms, 914

Geometric series
and branching patterns, 1005

Geometrical constructions
and history of universality, 1109
of real numbers, 1129
rules in, 875

Geometrical forms
in aggregation systems, 979
of artifacts, 835
in astronomy, 1187
in biology, 384
and diversity in biology, 395
on Earth seen from space, 1187
molecules made for their, 1194
of shocks in fluids, 1000

Geometrical optics, 1061

Geometrical Play
of Leonardo da Vinci, 875

Geometrical substitution systems, 189–192
implementation of, 933
visualizing evolution of, 933

Geometry
of animal shapes, 421
applied to biology, 1004
of attractors for ODEs, 961
axioms for, 774, 1154
as basis for science, 44
of branching patterns, 401
of cellular automaton lattices, 929
curvature in, 532
curves in Greek, 875
differential, 1048
as historical basis of math, 792
labelling in diagrams, 1182
and math in science, 859
network of theorems in Euclid's, 1176
non-universality in, 784
and origin of math, 859
in parametrizing biological forms, 1010
of plant phyllotaxis, 409
and proof in math, 1149
puzzles, 875
reasoning in terms of, 1177
rules for planet motion using, 860
of shell shapes, 417
space as uniform in early, 1028
of space of CA rules, 948
theorems and computational irreducibility, 1132

Geomorphology, 1001

Geons
and matter from gravity, 1054
and unified field theory, 1028

Gestalt (in psychology), 1076

Gestures
in animal communication, 1180
grammatical rules for, 1181

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