(Page 0897b) Notes for: The World of Simple Programs | Symbolic Systems Properties [of example symbolic system] All initial conditions eventually evolve to expressions of the ...

(Page 0759) whatever sequence of digits are left behind being taken to be the output of the computation. And what the pictures above show is that with this particular machine ...

(Page 1138d) Notes for: The Principle of Computational Equivalence | Undecidability and Intractability Undecidability and sets Functions that can be computed in finite time ...

(Page 0892f) Notes for: The World of Simple Programs | Substitution Systems Other examples [of substitution systems] (a) (Period-doubling sequence) After t steps, there are a ...

(Page 0904c) Notes for: Systems Based on Numbers | Elementary Arithmetic The 3 n+1 problem The system described here is similar to the so-called 3n+1 problem, in which one ...

(Page 1080i) Notes for: Processes of Perception and Analysis | Auditory Perception Spectra of substitution systems Questions that turn out to be related to spectra of ...

(Page 1143d) Notes for: The Principle of Computational Equivalence | Undecidability and Intractability [One-sided] Turing machines The Turing machines used here in effect ...