Labyrinth
pattern of, 873
Labyrinthine patterns
from 2D cellular automata, 427
in code 746, 334
Lag systems, 894
Lagrange, J. Louis (La Grange) (Italy/Germany/France, 1736-1813)
and continued fractions, 915
Lagrange points
simple geometry of, 1187
in three-body problems, 972
Lagrangian density
in general relativity, 1053
for PDEs, 923
in quantum field theory, 1061
LaguerreL (Laguerre polynomials)
in hydrogen atom, 1133
Lambda calculus, 1121
and Church's Thesis, 1125
and combinators, 1122
confluence in, 1036
and history of universality, 1110
as idealization of math, 1150
undecidability in, 1136
Lamé equations, 995
Laminar fluid flow, 376
in the atmosphere, 1001
Laminated sphere packings, 986
Land grants
and regular grid patterns, 1187
Land use
effects on weather of, 1177
Landau, Lev D. (Russia, 1908-1968)
and fluid turbulence, 997
Landau-Ginzburg equation, 925
Landscapes (abstract)
constraint satisfaction on, 346
for memory, 1101
Landscapes (geological), 1001
Langton, Christopher G. (USA, 1948- )
and 2D Turing machines, 930
and CA classes, 948
in Preface, xiii
Langton's ant (2D Turing machine), 931
Language games, 1181
Language of mathematics
and science, 859
Languages (abstract)
as attractors in TMs, 961
context-free, 939, 1091, 1103
context-sensitive, 939
regular, 939
universal and Leibniz, 1149
unrestricted, 939
see also Formal languages
Languages (computer), 1103
as examples of software, 1108
functional and combinators, 898
and history of computing, 1108
intuition from existence of, 872
logic programming, 1158
Mathematica, 853
meaning in, 1182
notion of types in, 898
for parallel computing, 1035
thinking in, 1104
universals in, 1182
see also Computer languages
Languages (human), 1103
as analogy in atomism, 876
animals trained to use, 826
center in brain, 1099
conventional aspect of, 1181
and cryptanalysis, 599
and defining intelligence, 822, 1178
frequency of words in, 1014
and history of universality, 1109
influence of on thinking, 1181
information content in, 1181
logic in everyday, 806, 1173
and math thinking, 1177
reasons for features of, 1181
recognizing meaning in, 826
redundancy of, 1086, 1181
relativity hypothesis in, 1181
rules for and programs, 860
rules in grammar for, 875
and theories of communication, 1181
and thinking, 630
translation of and AI, 1100
translation of and universality, 643
understanding dead, 1184
and Zipf's law, 1014
Laplace, Pierre-Simon (France, 1749-1827)
and Central Limit Theorem, 977
and determinism, 1135
Laplace equation
as constraint, 940
and diffusion-limited aggregation, 994
and flatness of growing tissue, 1007
and network dimensions, 1031
Laplacian
in curved space, 1050
LARC computer
and gas simulation, 864
Large cardinal axioms, 1167
Lasers
as technology components, 1195
Latencies
in circuits, 1095
Latent heat
and crystal growth, 370, 372
Lateral inhibition
and pigmentation patterns, 427
in plant phyllotaxis, 409
in snowflake growth, 370
Latin
logic operations in, 1173
Latin squares
and quasigroups, 1171
as satisfying constraints, 945
Lattice dynamical systems, 155-160, 922
see also Continuous cellular automata
Lattice gases, 999
enumeration in, 959
see also Cellular automaton fluids
see also Spin systems
Lattice gauge theories, 1057, 1061
and computational irreducibility, 1133
and discrete space, 1027
and quantum gravity, 1054
Lattice models
see also Cellular automata
see also Spin systems
Lattice packings, 987
Lattice points
numbers inside spheres, 910
Lattice theory
axioms for, 1153
and posets, 1041
|  | Lattice vectors
and linear congruential generators, 974
LatticeReduce
and digit sequence cryptanalysis, 1089
Lattices
isotropic behavior on, 980
lines at slopes on, 916
possible, 929
random walks on, 329, 977, 978
Law of large numbers, 976
Laws (human)
and defining randomness, 1068
and free will, 1135
and regularities in radio spectrum, 1188
and responsibility, 1136
Laws of Form
and Nand, 1173
Laws of physics
vs. mathematics, 772
vs. programs in biology, 397
and ultimate theory, 470
Layout of networks, 193
NP completeness of, 1145
LCDs
see Liquid crystals
LCGs
see Linear congruential generators
LCM (lowest common multiple)
and Lissajous figures, 917
and Riemann Hypothesis, 918
Leading digits, 914
and number compression, 1070
of powers, 903
Leaf shapes
see Leaves
LeafCount (expression size)
and algebraic expressions, 945
and combinator expressions, 1122
and number of recursive functions, 908
and symbolic systems, 897
for universal Diophantine equation, 1161
Learning
of bird songs, 1180
of computer languages, 1104
and defining intelligence, 823, 1178
human, 626
models of, 1099, 1102
the science in this book, 855
as trick in evolution, 1002
Learning curves, 1014, 1102
Least squares fitting, 1082, 1083
Leaves
arrangements of (phyllotaxis), 408-412, 1006
evolutionary theories of, 1005
flatness in growth of, 1008
growth of, 401, 412, 1005
shapes of, 401-407, 1005
LED segments
and textons, 1076
Leech lattice
isotropy of, 980
and sphere packings, 987
Leftmost innermost evaluation, 906
Leg (animal)
development of, 419
Legendre, Adrien-Marie (France, 1752-1833)
and sums of three squares, 910
LegendreP (Legendre polynomials)
and isotropy measures, 980
in solution of Mie scattering, 1133
Lehmer, Derrick H. (USA, 1905-1991)
and linear congruential generators, 974
Lehr, Eduard (Germany, ~1932)
and parametric curves, 1009
Leibniz, Gottfried W. v. (Germany, 1646-1716)
and binary numbers, 902
and calculators, 1107
and free will, 1135
and I Ching, 893
and idealizations of math, 1149
and logic, 1099
and logic as basis for science, 860
and math notation, 1182
and the nature of space, 1028
and origins of universality, 1109
and symbolic logic, 1151
and universal language, 1181
Lemmas
defining characteristics of, 1176
and lengths of proofs, 1175
in proof of axiom for logic, 811
in proof searching, 1157
in structure of proofs, 1155
Lempel, Abraham (Israel, 1936- )
and data compression, 1069
Lempel-Ziv encoding, 565
Lemur
pigmentation pattern on, 426
Length
basic example of, 853
Lenses
characteristic shapes of, 1183
Lenticular clouds, 1183
Lenz, Wilhelm (Germany, 1888-1957)
and Ising model, 981
Leonardo da Vinci
see da Vinci, Leonardo
Leopard
pigmentation pattern of, 426
Leptons
as types of particle, 1043
Less (<)
encoded as integer equation, 1160
Letters
frequencies of in English, 1069
visual perception of, 1076
Lettuce
ammonite septa like, 1008
growth of, 413
Leucippus (Greece, ~480 - ~420 BC)
and atomism, 876
Levin, Leonid A. (Russia/USA, 1948- )
and NP completeness, 1143
in Preface, xiii
and transitions in CAs, 981
Lévy, Paul P. (France, 1886-1971)
and nested C curve, 893, 934
Lévy flights, 969
lex
and regular languages, 958
Lexical analysis
and regular languages, 958
LFSRs (linear feedback shift registers)
see Shift registers
LHASA (chemical synthesis software), 1194
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