(Page 0920a) Notes for: Systems Based on Numbers | Iterated Maps and the Chaos Phenomenon Mathematical perspectives [on iterated map complexity] Mathematicians may be ...

(Page 0903d) Notes for: Systems Based on Numbers | Elementary Arithmetic General powers [of numbers] It has been known in principle since the 1930s that Mod[h ^ n , 1] is ...

(Page 0956c) Notes for: Starting from Randomness | Special Initial Conditions Uniqueness of patterns [in cellular automata] Starting from a particular initial condition, ...

(Page 0058) Repetition and nesting are widespread themes in many cellular automata. But as we saw in the previous chapter , it is also possible for cellular automata to ...

(Page 0146) In the third picture, however, the points where the curve crosses the axis come in two regularly spaced families. And as the pictures on the facing page indicate, ...

(Page 0905e) Notes for: Systems Based on Numbers | Elementary Arithmetic Iterated run-length encoding Starting say with {1} consider repeatedly replacing list by (see page ...

(Page 0959a) Notes for: Starting from Randomness | The Notion of Attractors 2D generalizations [of entropies] Above 1D no systematic method seems to exist for finding exact ...

(Page 0978a) Notes for: Mechanisms in Programs and Nature | The Phenomenon of Continuity Self-avoiding [random] walks Any walk where the probabilities for a given step depend ...

(Page 0986b) Notes for: Mechanisms in Programs and Nature | The Problem of Satisfying Constraints [Sphere packings in] higher dimensions In no dimension above 3 is it known ...

(Page 1129b) Notes for: The Principle of Computational Equivalence | The Validity of the Principle Constructible reals Instead of finding successive digits using systems like ...