# Index

`I-1`

base, 932

I Ching

and substitution systems, 893

IBM 370 computer

my use of, 854

IBM 7090 computer

and pi, 911

ICBMs

radar used by, 970

radars for detecting, 1188

Ice

hopper crystals in, 993

snowflake crystals of, 370

Ice-ray style of Chinese lattice, 874

Icosahedral group, 938

Icosahedral symmetry

in quasicrystals, 994

Icosahedron

clusters in sphere packing, 986

and `GoldenRatio`

, 891

IDEA cryptographic system, 1086

Ideal forms

and Platonism, 1176

Ideal gas

CA idealization of, 446

Idealism

and free will, 1135

and history of universality, 1109

and logic as foundation, 860

and models of math, 1149

and nature of space, 1028

and theories of communication, 1181

and universe as intelligence, 1196

Idealizations

of mathematics, 776

in modelling, 364

and Principle of Computational Equivalence, 728

in traditional science, 736

and ultimate theory of physics, 465

Ideals (algebraic)

as generalizing numbers, 1168

Idempotence

of `And`

, 817

in operator systems, 801

of `Or`

, 817

Identity cellular automaton, 883

Identity function

in combinators, 1122

IEEE floating-point standard

and chaos experiments, 919

`If`

(conditional)

emulated by `Gamma`

, 1129

Illative logic

and symbolic systems, 102

ILLIAC IV

and history of CAs, 877

Illinois, University of, xiii

Illusions

visual, 1076

Image compression

lossless, 560

lossy, 572

Image processing

by averaging, 1073

history of, 1077

and history of 2D CAs, 877, 928

and visual perception, 1076

and Walsh transforms, 1073

Imaginary time formalism, 1043

as example of model feature, 992

Imitation

and bird songs, 1180

see also Emulation

Immune system

and Boolean networks, 936

and combinatorial chemistry, 1194

and growth of animals, 418

randomness in, 970, 1002

shape space in, 1184

Impact craters

as landscape elements, 1001

Implementation

see also Emulation

see also entries for specific systems

Implicants

in Boolean formulas, 1095

Implicational calculus, 803, 1170

models in, 1171

possible models of, 805

theorems in, 813

Implicit rules

constraints as, 210, 940

`Implies`

axioms for, 803

axioms in terms of, 1151

in multivalued logic, 1175

non-confluence of, 1037

non-universality of, 1174

and structure of proofs, 1155

truth tables for, 802

Impossibilities

mathematical, 1137

Impulse response

for additive systems, 952

spectrum of, 1081