(Page 0876a) Notes for: The Crucial Experiment | Why These Discoveries Were Not Made Before Atomism The idea that everything might be made up from large numbers of discrete ...

(Page 0888e) Notes for: The World of Simple Programs | Turing Machines Distribution of behavior [in Turing machines] With 2 possible states and 2 possible colors for each ...

(Page 0896g) Notes for: The World of Simple Programs | Symbolic Systems Symbolic expressions Expressions like Log[x] and f[x] that give values of functions are familiar from ...

(Page 0905a) Notes for: Systems Based on Numbers | Elementary Arithmetic A reversible [3n+1 problem] system In both the ordinary 3n+1 problem and in the systems discussed in ...

(Page 0906b) Notes for: Systems Based on Numbers | Recursive Sequences Recurrence relations The rules for the sequences given here all have the form of linear recurrence ...

(Page 0909e) Notes for: Systems Based on Numbers | The Sequence of Primes History of number theory Most areas of mathematics go from inception to maturity within at most a ...

(Page 0928d) Notes for: Two Dimensions and Beyond | Cellular Automata History [of 2D cellular automata] As indicated on pages 876 - 878 , 2D cellular automata were ...

(Page 0943d) Notes for: Two Dimensions and Beyond | Systems Based on Constraints Polyominoes An example of a tiling problem that is in some respects particularly close to the ...

(Page 0963c) Notes for: Starting from Randomness | The Notion of Attractors [State networks for] additive rules The pictures below show networks obtained for the additive ...

(Page 1002h) Notes for: Implications for Everyday Systems | Fundamental Issues in Biology Smooth variables [in biology] Despite their importance in understanding natural ...