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ix
1
The Foundations for a New Kind of Science
1
Section 1: An Outline of Basic Ideas
1
Section 2: Relations to Other Areas
7
Section 3: Some Past Initiatives
12
17
2
The Crucial Experiment
23
Section 1: How Do Simple Programs Behave?
23
Section 2: The Need for a New Intuition
39
Section 3: Why These Discoveries Were Not Made Before
42
3
The World of Simple Programs
51
Section 1: The Search for General Features
51
Section 2: More Cellular Automata
53
Section 3: Mobile Automata
71
Section 4: Turing Machines
78
Section 5: Substitution Systems
82
Section 6: Sequential Substitution Systems
88
Section 7: Tag Systems
93
Section 8: Cyclic Tag Systems
95
Section 9: Register Machines
97
Section 10: Symbolic Systems
102
Section 11: Some Conclusions
105
Section 12: How the Discoveries in This Chapter Were Made
108
4
Systems Based on Numbers
115
Section 1: The Notion of Numbers
115
Section 2: Elementary Arithmetic
117
Section 3: Recursive Sequences
128
Section 4: The Sequence of Primes
132
Section 5: Mathematical Constants
136
Section 6: Mathematical Functions
145
Section 7: Iterated Maps and the Chaos Phenomenon
149
Section 8: Continuous Cellular Automata
155
Section 9: Partial Differential Equations
161
Section 10: Continuous Versus Discrete Systems
167
5
Two Dimensions and Beyond
169
Section 1: Introduction
169
Section 2: Cellular Automata
170
Section 3: Turing Machines
184
Section 4: Substitution Systems and Fractals
187
Section 5: Network Systems
193
Section 6: Multiway Systems
204
Section 7: Systems Based on Constraints
210
6
Starting from Randomness
223
Section 1: The Emergence of Order
223
Section 2: Four Classes of Behavior
231
Section 3: Sensitivity to Initial Conditions
250
Section 4: Systems of Limited Size and Class 2 Behavior
255
Section 5: Randomness in Class 3 Systems
261
Section 6: Special Initial Conditions
266
Section 7: The Notion of Attractors
275
Section 8: Structures in Class 4 Systems
281
7
Mechanisms in Programs and Nature
297
Section 1: Universality of Behavior
297
Section 2: Three Mechanisms for Randomness
299
Section 3: Randomness from the Environment
301
304
Section 5: The Intrinsic Generation of Randomness
315
Section 6: The Phenomenon of Continuity
327
Section 7: Origins of Discreteness
337
Section 8: The Problem of Satisfying Constraints
342
Section 9: Origins of Simple Behavior
351
8
Implications for Everyday Systems
363
Section 1: Issues of Modelling
363
Section 2: The Growth of Crystals
369
Section 3: The Breaking of Materials
374
Section 4: Fluid Flow
376
Section 5: Fundamental Issues in Biology
383
Section 6: Growth of Plants and Animals
400
Section 7: Biological Pigmentation Patterns
422
Section 8: Financial Systems
429
9
Fundamental Physics
433
Section 1: The Problems of Physics
433
Section 2: The Notion of Reversibility
435
441
Section 4: Conserved Quantities and Continuum Phenomena
458
Section 5: Ultimate Models for the Universe
465
Section 6: The Nature of Space
472
Section 7: Space as a Network
475
Section 8: The Relationship of Space and Time
481
Section 9: Time and Causal Networks
486
Section 10: The Sequencing of Events in the Universe
497
Section 11: Uniqueness and Branching in Time
504
Section 12: Evolution of Networks
508
Section 13: Space, Time and Relativity
516
Section 14: Elementary Particles
525
Section 15: The Phenomenon of Gravity
530
Section 16: Quantum Phenomena
537
10
Processes of Perception and Analysis
547
Section 1: Introduction
547
Section 2: What Perception and Analysis Do
548
Section 3: Defining the Notion of Randomness
552
Section 4: Defining Complexity
557
Section 5: Data Compression
560
Section 6: Irreversible Data Compression
572
Section 7: Visual Perception
577
Section 8: Auditory Perception
585
Section 9: Statistical Analysis
588
Section 10: Cryptography and Cryptanalysis
598
606
Section 12: Human Thinking
620
Section 13: Higher Forms of Perception and Analysis
632
11
The Notion of Computation
637
Section 1: Computation as a Framework
637
Section 2: Computations in Cellular Automata
638
Section 3: The Phenomenon of Universality
642
Section 4: A Universal Cellular Automaton
644
656
664
Section 7: Implications of Universality
674
Section 8: The Rule 110 Cellular Automaton
675
Section 9: The Significance of Universality in Rule 110
690
Section 10: Class 4 Behavior and Universality
691
694
706
12
The Principle of Computational Equivalence
715
Section 1: Basic Framework
715
Section 2: Outline of the Principle
716
Section 3: The Content of the Principle
719
Section 4: The Validity of the Principle
726
Section 5: Explaining the Phenomenon of Complexity
735
Section 6: Computational Irreducibility
737
Section 7: The Phenomenon of Free Will
750
Section 8: Undecidability and Intractability
753
772
Section 10: Intelligence in the Universe
822
Section 11: Implications for Technology
840
Section 12: Historical Perspectives
844
Notes
849
859
Notes 2: The Crucial Experiment
865
Notes 3: The World of Simple Programs
883
Notes 4: Systems Based on Numbers
901
Notes 5: Two Dimensions and Beyond
927
Notes 6: Starting from Randomness
947
Notes 7: Mechanisms in Programs and Nature
967
Notes 8: Implications for Everyday Systems
991
Notes 9: Fundamental Physics
1017
Notes 10: Processes of Perception and Analysis
1067
Notes 11: The Notion of Computation
1107
1125
Notes from the Book
The complete notes section from the book reformatted with larger text size.
The complete notes section from the book reformatted with larger text size.
