Object-oriented programming, 867
Object recognition, 624
Objects
described by axiom systems, 797
and image compression, 1074
Observables
in quantum mechanics, 1056
Observational errors
and Gaussian distribution, 977
and origin of randomness, 967
Observers
and Anthropic Principle, 1026
computational abilities of, 737
definition of particles for, 1062
and origin of causal networks, 487
Occam's razor, 1025
Ocean currents
and weather, 1177
Ocean waves, 1001
as example of randomness, 301
nested breaking of, 997
pattern formation in, 947
repetitive behavior in, 988
Oceans
exploration of, 1191
finding artifacts under, 1183
whale songs in, 1180
Ocelot
pigmentation pattern of, 426
OCR (optical character recognition)
and cellular automata, 877
Octahedra
extraterrestrial in 2001, 1190
truncated, 930, 987
Octanes, 1194
Octaves (in music), 917, 1079
Octonions
as generalizing numbers, 1168
Octopus
communication by, 1181
form of tentacles of, 385
visual system of, 1075
Ocular dominance stripes
CA model for, 1012
maze-like patterns in, 1013
in visual system, 1075
OddQ (test for odd numbers)
and nested patterns, 931
and rule 132, 638
Odds and Evens game, 1105
ODEs, 922
see also Ordinary differential equations
Odlyzko, Andrew M. (USA, 1949- )
and additive CAs, 951
as coauthor of paper, 881
in Preface, xiii
and zeros of zeta function, 918
Odometer
and history of computing, 1107
Odor perception, 1105
and experience of dogs, 827
Offset lists
in general cellular automata, 927
OH (hydroxyl) frequency, 1189
Oil and water
separation of, 980
Oil fires
patterns in, 377
visible from space, 1187
Olaus Magnus (Sweden/Italy, 1490-1568)
and snowflakes, 992
Olbers' paradox, 1021
Old English
logic operations in, 1173
Olfactory perception, 1105
and experience of dogs, 827
Olive shell
growth of, 415
Omega (halting probability), 1067
omega (first transfinite ordinal), 1162
One-sided additivity
and cryptography, 1088
repetition from, 954
One-time pad (in cryptography), 1086
One-to-one mapping (injective), 960
Ones
expressing numbers with, 916
number of (DigitCount), 902
Onsager, Lars (USA, 1903-1976)
and 2D Ising model, 982
Onto cellular automata, 280, 959
Ontology
implications for, 1197
and notions of space, 1028
Opcodes
in practical computers, 1108
in register machines, 896
Open sets
and axioms of topology, 1155
Open systems
and thermodynamics, 455
Operating systems
and concept of halting, 1137
and history of computing, 1108
in practical computers, 1108
Operation counts in computations, 1143
Operator representations
for integers, 916
Operator systems, 801
automated proofs in, 1158
evolution rules for, 898
frameworks for proofs in, 1177
vs. multiway systems, 1169
Operators
as generalizing numbers, 1168
notation for, 1182
possible Boolean, 806
precedence of, 1104
precedence of in math, 1150
in quantum theory, 1056
Optic nerve, 1075
Optical amplifier, 310
Optical character recognition (OCR)
and history of CAs, 877
Optical computing
CA implemented with, 869
and quantum computers, 1148
Optical fibers
as technology component, 1195
Optical illusions, 1076
Optical SETI, 1189
Optics
and history of math in science, 859
path integral in, 1061
Optimal algorithms, 1141
Optimal evaluation chains, 1095
|  | Optimality
and defining purpose, 829
and models of markets, 1015
Optimization
combinatorial, 985
and complexity in biology, 398
of designs in engineering, 1193
intuition about in programs, 872
and Occam's razor, 1025
in plant leaf arrangements, 408
Optimized circuit blocks, 1193
Optimizers
and proofs about programs, 1168
search strategies in, 1193
Options
market prices of, 1015
Or
axioms in terms of, 1151
and Boolean formulas, 1095
calculus of expressions, 1170
emulated by CAs, 662, 1112
encoded as integer equation, 1160
in multivalued logic, 1175
and P completeness, 1149
and satisfiability, 1146
table for, 806
theorems involving, 817
words in languages for, 1173
Oracles (in computation theory), 1126
and arithmetic hierarchy, 1139
based on infinite tables, 720
and intermediate degrees, 1131
and non-standard arithmetic, 1169
and second-order logic, 1167
Orbits
in Bohr atom, 1056
of comets and Gaussians, 977
and history of computing, 1107
randomness in, 313
as simple shapes, 1187
in three-body problem, 972
Order
emergence from randomness, 223
Order diagrams of posets
and causal networks, 1040
Order of updates
in sequential CAs, 1034
in sequential substitution systems, 894
in string rewriting, 497
in symbolic systems, 898
see also Causal invariance
Order parameters
in phase transitions, 981
Ordered fields
axioms for, 1153
Orderless (commutative)
and associative CAs, 956
Boolean functions, 1173
and generalized additivity, 952
and speedups in evolution, 1095
Orders of infinity, 1127, 1162
Ordinal numbers
and encoding of proofs, 1163
as generalizing numbers, 1168
and notions of infinity, 1162
Ordinary differential equations (ODEs), 922
for chemical processes, 1013
Oresme, Nicole (France, ~1320-1382)
and time as a dimension, 1031
Organic molecules
production of, 1179
Organization
see Self-organization
Organizational structures
and history of complexity, 862
and Occam's razor, 1025
Organogenesis in plants, 409
Organs
and biological evolution, 389, 1002
separate rules for different, 383
Origami (paperfolding)
NP completeness in, 1145
rules in, 875
Origin of Species, 1001
Ornament
examples of, 43
grammatical rules in, 1181
and notion of purpose, 830
rules in, 872
and theory of form, 967
Orreries, 1184
Orthogonal bases, 1072
and image compression, 573
and radio signals, 1188
Oscillations
in chemical reactions, 1013
of density in rule 73, 954
in fluid flow, 998
in math functions, 917, 1134
origins of, 354-356
in PDEs, 988
Oscillators
in Game of Life, 964
nonlinear, 971
in quantum history, 1056
Oseen, C. William (Sweden, 1879-1944)
and fluid flow past spheres, 998
Oster, George F. (USA, 1940- )
and patterns on shells, 1012
in Preface, xiii
Other minds
problem of recognizing, 1197
Otter (theorem-proving system), 1158
Outer
and branching patterns, 1005
and enumerating expressions, 897
and metrics on surfaces, 1048
and shape tensors, 980
Outer totalistic rules
in cellular automata, 928
Outlying data, 1083
Overlaps
in networks, 510
in strings, 503, 1033
Overshooting
in gradient descent, 985
Ozsváth-Schücking rotating vacuum, 1053
P = NP problem, 765
and SETI, 1190
and systems in nature, 770
undecidability of, 1146
P (polynomial time), 1142
p-adic numbers
as generalizing numbers, 1168
P-code for GPS, 1086
P completeness, 1149
|
Send a Message
