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Chapter 3:
The World of Simple Programs
Section 1:
The Search for General Features
There are no notes for this section.
Section 2:
More Cellular Automata
[History of] numbering scheme
Rule equivalences [for cellular automata]
Special [cellular automaton] rules
Rule expressions [for cellular automata]
Rule orderings [for cellular automata]
Algebraic forms [for cellular automaton rules]
Rule 150
Rule 225
Rule 22
Algebraic forms [for cellular automaton rules]
Rule 45
Rule 73
Alternating colors
[Cellular automata with] two-cell neighborhoods
Numbers of [cellular automaton] rules
Implementation of general cellular automata
Implementation of totalistic cellular automata
Common framework [for cellular automaton rules]
Mod 3 [cellular automaton] rule
Compositions of cellular automata
[Cellular automaton] rules based on algebraic systems
Section 3:
Mobile Automata
Implementation [of mobile automata]
Compressed evolution [of mobile automata]
Distribution of behavior [in mobile automata]
Active cell motion [in mobile automata]
Implementation of generalized mobile automata
Section 4:
Turing Machines
Implementation [of Turing machines]
Number of [Turing machine] rules
Numbering scheme [for Turing machines]
Counter [Turing] machine
Distribution of behavior [in Turing machines]
Head motion [in Turing machines]
Localized structures [in Turing machines]
History [of Turing machines]
Section 5:
Substitution Systems
Implementation [of substitution systems]
Properties [of substitution systems]
Growth rates [in substitution systems]
Fibonacci numbers
Lucas numbers
Generalized Fibonacci sequences
Connections [of substitution systems] with digit sequences
Connections [of substitution systems] with square roots
Spectra of substitution systems
Representation [of substitution systems] by paths
Paperfolding sequences
2D representations [of substitution systems]
Other examples [of substitution systems]
History [of substitution systems]
Section 6:
Sequential Substitution Systems
Implementation [of sequential substitution systems]
Capabilities [of sequential substitution systems]
Order of replacements [in sequential substitution systems]
History [of sequential substitution systems]
Section 7:
Tag Systems
Implementation [of tag systems]
Randomness [in tag systems]
History [of tag systems]
Section 8:
Cyclic Tag Systems
Implementation [of cyclic tag systems]
Generalizations [of cyclic tag systems]
Mechanical implementation [of cyclic tag systems]
Properties [of cyclic tag systems]
History [of cyclic tag systems]
Section 9:
Register Machines
Implementation [of register machines]
Halting [of register machines]
Extended instruction sets [for register machines]
History [of register machines]
Random programs
Section 10:
Symbolic Systems
Implementation [of symbolic systems]
Symbolic expressions
Representations [for symbolic expressions]
[Enumerating] possible expressions
Properties [of example symbolic system]
Other [symbolic systems] rules
Long halting times [in symbolic systems]
Trees [representation for symbolic systems]
Order dependence [in symbolic systems]
History [of symbolic systems]
Operator systems
Network analogs [of symbolic systems]
Section 11:
Some Conclusions
There are no notes for this section.
Section 12:
How the Discoveries in This Chapter Were Made
Repeatability and numerical analysis
Studying simple systems
The relevance of theorems
Attitudes of mathematicians
History of experimental mathematics
Practicalities [of computer experiments]