Index



Fabric
wrinkling of, 996

Face-centered cubic (fcc)
lattice, 930
sphere packing, 986
Voronoi diagram, 987

Faces (geometrical)
in deformable packings, 988
and discrete spaces, 1051
in planar networks, 1038

Faces (human)
development of bones in, 1010
parametrization of, 1010
random variations in, 1192
recognition of, 626

Faceted crystal growth, 370

Factor (polynomial factorization)
analog for Boolean formulas, 1095
and cycles in shift rules, 963
and quadratic congruential generators, 975
randomized algorithm for, 1192
and shift register periods, 975

Factorial (n!)
encoded as integer equation, 1160
and examples of universality, 1110
and hypersphere volume, 1050
leading digits in, 914
and number of reversible block cellular automata, 1023
number with digits at, 914
and QED perturbation series, 1060
as recursive sequence, 906
and transcendental numbers, 914
see also Gamma

Factorial2 (double factorial)
and isotropic tensors, 980

Factories
and self-reproducing systems, 876

FactorInteger (integer factorization)
and arithmetic system encoding, 1115
basic methods for, 1090
difficulty of evaluating, 1134
and Fermat's Last Theorem, 1166
and multiplicative digit sequences, 902
and MultiplicativeOrder, 1147
and NP completeness, 1146
and number of commutative groups, 1172
and quantum computers, 1148
running times for, 1090
unique domains for, 915

Factorization
of cellular automata, 956

False
definition from And and Not, 817

Falsifiability of models, 365

Faltings theorem (Mordell conjecture), 1164

Family trees
and substitution systems, 893

Fano, Robert M. (USA, 1917- )
and data compression, 1069

Farey sequences, 916

Farm animals
growth of, 1010

Fast algorithms, 1141

Fast Fourier transform (FFT)
recursive algorithm for, 1142
see also Fourier

Fast Walsh transform, 1073

Fastest programs, 760

Fate
vs. randomness, 967, 1135

Fax
data compression in, 1070

fcc (face-centered cubic)
lattice, 930
sphere packing, 986
Voronoi diagram, 987

Feasible computations, 1143
see also Polynomial time

Feathers
coloration of, 1012

Feature detection
as basis for perception, 549
in human visual system, 577

Fedorov, Evgraf S. (Russia, 1853-1919)
and shapes of 3D domains, 929

Feedback
control and cybernetics, 862
in growth of bones, 1010
in visual system, 1075

Feedback shift registers, 974
see also Shift registers

Feigenbaum, Mitchell J. (USA, 1944- )
and computer experiments, 899
and iterated maps, 921
in Preface, xiii

Feigenbaum's constant, 913

Fejes Tóth, László (Hungary, 1915- )
and circle packing, 985

Fermat, Pierre de (France, 1601-1665)
and Fermat's Last Theorem, 1166
and primes, 909

Fermat primes conjecture
as unsolved problem, 1166

Fermat's Last Theorem, 1166
and Diophantine equations, 1164
as having long proof, 779
and number theory history, 910
and sparse solutions, 945

Fermat's little theorem, 909

Fermat's principle (in optics), 1061

Fermi, Enrico (Italy/USA, 1901-1954)
and computer experiments, 879, 899
and extraterrestrial contact, 1191
and statistical mechanics, 1020

Fermi-Pasta-Ulam experiment, 1020

Fermilab
circular shape of, 1187

Fermions
and basic quantum effects, 1059
and classical limits, 1059
spin-statistics of, 1046

Ferns
branching in, 401, 1004
and iterated function systems, 1005

Ferrite core memory, 864

Ferrites
as components in technology, 1195

Ferrofluids
maze-like patterns in, 1013
phyllotaxis-like patterns in, 1007

Ferromagnetic materials
Ising model for, 981
phase transitions in, 981

Fertilization
randomness in, 970

Feynman, Carl R. (USA, 1962- )
and cryptanalysis of rule 30, 1087
in Preface, xiii

Feynman, Richard P. (USA, 1918-1988)
and cryptanalysis of rule 30, 1087
and discrete quantum models, 1060
and discreteness of space, 1027
and path integrals, 1057
and physics and computation, 1126
in Preface, xii, xiii, xiv

Feynman diagrams, 1060
exact calculations of, 1133
history of, 1057
Monte Carlo methods in, 1192
not as mechanistic model, 1026
in QCD, 1061
for quantum gravity, 1054
and random networks, 1039
vs. space networks, 1040
and spin networks, 1055

FFT (fast Fourier transform)
digit reversal sequences in, 905
implementation of, 1074
multiplication using, 1093
recursive algorithm for, 1142
see also Fourier

Fiber bundles
and continuum limits of networks, 1030
and gauge theories, 1045

Fiber optics
vs. broadcasting, 1188

Fibers (biological)
and folding of tissue, 417

Fibonacci, Leonardo (Pisano) (Italy, ~1170 - ~1250)
and digital numbers, 902
and Fibonacci numbers, 891
and rabbit populations, 1002
and tables of primes, 910
and trees, 893

Fibonacci (Fibonacci sequence)
difficulty of making with CAs, 1186
and entropy in rule 32, 958
generalized, 891
generalized for randomness generation, 975
generating function for, 1091
as initial condition for rule 60, 1091
leading digits in, 914
and multiway system states, 205
and multiway systems based on numbers, 939
number with digits at, 914, 1070
in ordering of math constructs, 1177
and plant phyllotaxis, 1006
and polyominoes, 943
as precursors to my work, 878
properties of, 890
and prosody, 875
and randomness generators, 975
and recursion history, 907
as recursive sequence, 128
and rule 150 pattern, 885
as solution to Diophantine equation, 1161
and spectral maxima, 1081
and substitution systems, 82, 890
as term in continued fraction, 913
uniform distribution mod 1, 904
as values of polynomial, 1161

Fibonacci multiway system, 205

Fibonacci number representation, 560, 1070
and multicolor encodings, 1111
as non-power base, 902
and substitution systems, 892

Fibonacci substitution system, 83
and cyclic tag system, 895
and cyclic tag systems, 96
in music, 875
and Penrose tilings, 932
properties of, 890
and sine curves, 147
spectrum of, 586, 1081
two-dimensional, 932

Field Museum of Natural History, 1011

Field operators
measurement of, 1065

Field theory (in abstract algebra), 1153
axioms for, 773
decidability with ordering predicates, 1159
and generalizing numbers, 1168
universality of, 1159
see also Finite fields

Field theory (physics)
history of, 1024
nonlinear PDE as, 923
quantum, 1061
see also Quantum field theory

Fields (agricultural)
patterns of from space, 1187

Fifths (musical chords)
curves of, 146
perfect, 1079

Fig leaves, 1005

Figurate numbers, 911

Filters (for data)
cellular automata as, 225
in visual perception, 1076

Filters in posets, 1040

Final cause, 1185

Final theory
see Ultimate theory of physics

Financial systems
applications to, 429-432
data from as source of randomness, 969
history of models of, 1015
meaning of random data in, 1183
simulations of, 968
using randomness to verify contracts in, 968

FindMinimum
and network layouts, 1031

FindRoot
difficulty of evaluating, 1134
iterative algorithm for, 1141

Fine structure constant (alpha)
numerology for, 1025
and perturbation theory, 1057

Fine tuning
and self-organized criticality, 989

Fingerprints
origin of patterns in, 1013
randomness in, 1014

Fingers
formation of human, 419

Finite automata
and attractors for CAs, 277
and Boolean functions, 1097
and CA encodings, 1119
and defining complexity, 1069
and formulas for nesting, 608
and groups, 1141
history of, 958
lower bounds in, 1143
minimization of, 957
as networks, 957
probabilistic, 1084
and regular languages, 939
and semigroups, 1153
and soundex system, 1100
spectra of, 1081
and substitution systems, 891, 931, 1091
total number of, 957

Finite axiomatizability, 1176

Finite complement languages, 941
2D generalizations, 959
and excluded blocks, 958
and repetition in 1D CAs, 954

Finite differences
and CA diffusion, 1024
and continuous CAs, 921
explicit schemes and sequential cellular automata, 1035
and history of CAs, 876
isotropy in, 980
methods based on, 940
neighborhood compared to cellular automata, 928
for PDEs, 924
and reaction-diffusion, 1013

Finite element methods, 940

Finite fields
as not universal, 1160
see also Additive cellular automata
see also Field theory (in abstract algebra)

Finite groups
axioms for, 1176
Cayley graphs of, 1032
as extraterrestrial messages, 1190
rules for, 938

Finite impulse response
and sequential CAs, 1035

Finite-size scaling
in Ising models, 983

Finite-size systems, 255-260, 961

Finite state machines
see Finite automata

Finitely presented groups
see Groups

Finitistic mathematics, 1158

Finkelstein, David R. (USA, 1929- )
and discreteness of space, 1027
in Preface, xiii

Finnish
logic operations in, 1173

Fins (heat exchanger)
characteristic shapes of, 1183

Fire
as artifact, 1183
as basis for universe, 1125
as visible from space, 1187

Firing of neurons
in neural networks, 1102
repeatable randomness in, 976

Firing squad problem (in cellular automata), 876, 1035

First digits, 914
of powers, 903

First Law of Thermodynamics, 1019

First-order phase transitions, 981

Fisher, Ronald A. (England, 1890-1962)
and random number tables, 968

Fisher-Tippett distribution, 977

Fishes
color vision in, 1075
iterated maps for populations of, 918
pigmentation patterns of, 389, 426
shapes of related by transformations, 1010

Fishhooks
characteristic shapes of, 1183

Fit (least-squares fit), 1083

Fitness
optimization of in biology, 386
and purpose, 1185

Fitting
of models, 589, 1083

Fitting of clothes
and allometry, 1010

FitzGerald, George F. (Ireland, 1851-1901)
and relativity theory, 1041

FitzGerald-Lorentz contraction, 1041

Five-body problem, 1130

Five-fold symmetry
in biology, 1007
cellular automata with, 930
and Penrose tilings, 932, 943
in quasicrystals, 994

Five-neighbor rules (in CAs), 927

Fixed points
in 1D cellular automata, 224, 954
in 2D cellular automata, 954
as attractors, 276
of blocking transformations, 270, 955
in combinator evolution, 712, 1122
for differential equations, 961
in Game of Life, 964
in iterated maps, 955, 961
in Mathematica, 1137
of pigmentation patterns, 427
in recursive evaluation, 906
of sandpile model, 989
and satisfying constraints, 348
in symbolic systems, 897
undecidability of, 1138

FixedPoint
and gradient descent, 985
undecidability in, 1138

FixedPointList
and length prefixed numbers, 1070
and prime implicants, 1095

Flagellated microorganisms
random motion of, 970

Flames
as self-organizing systems, 824
as self-reproducing, 1178

Flash photography
and forms of splashes, 1000

Flat (associative)
and associative CAs, 886, 956
and Boolean functions, 1173
and confluence property, 1037
and fast evolution rules, 1094
and generalized additivity, 952
and sequential substitution systems, 894

Flat spectra, 1081

Flatness (geometry)
of growing sheets of tissue, 1007

Flatten
basic examples of, 853
and correspondence systems, 1139
generalized to 2D, 931, 1073
generalized to any dimension, 932
and sequence equations, 944, 1141

Flatworm
pigmentation pattern on, 426

Flicker noise, 969
see also 1/f noise

Flint arrowheads, 1183