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Notes for: Starting from Randomness   (Stephen Wolfram's "A New Kind of Science")
(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 ...
Notes for: Systems Based on Numbers   (Stephen Wolfram's "A New Kind of Science")
(Page 0911b) Notes for: Systems Based on Numbers | The Sequence of Primes Other integer functions IntegerExponent[n, k] gives nested behavior as for decimation systems on ...
Notes for: The Principle of ...   (Stephen Wolfram's "A New Kind of Science")
(Page 1145b) Notes for: The Principle of Computational Equivalence | Undecidability and Intractability [Turing] machine 600720 (Case (h) of page 763 .) The maximum halting ...
Notes for: Systems Based on Numbers   (Stephen Wolfram's "A New Kind of Science")
(Page 0902c) Notes for: Systems Based on Numbers | Elementary Arithmetic Digit counts The number of black squares on row n in the pattern shown here is given by ...
Notes for: Starting from Randomness   (Stephen Wolfram's "A New Kind of Science")
(Page 0955b) Notes for: Starting from Randomness | Special Initial Conditions Sarkovskii's theorem For any iterated map based on a continuous function such as a polynomial it ...
Notes for: Systems Based on Numbers   (Stephen Wolfram's "A New Kind of Science")
(Page 0906e) Notes for: Systems Based on Numbers | Recursive Sequences Properties of [recursive] sequences Sequence (d) is given by f[n_] := (n + g[IntegerDigits[n, 2]])/2 ...
Notes for: The World of Simple Programs   (Stephen Wolfram's "A New Kind of Science")
(Page 0885c) Notes for: The World of Simple Programs | More Cellular Automata Rule 150 This rule can be viewed as an analog of rule 90 in which the values of three cells, ...
Notes for: Systems Based on Numbers   (Stephen Wolfram's "A New Kind of Science")
(Page 0909b) Notes for: Systems Based on Numbers | The Sequence of Primes Decimation systems A somewhat similar system starts with a line of cells, then at each step removes ...
Notes for: Starting from Randomness   (Stephen Wolfram's "A New Kind of Science")
(Page 0950c) Notes for: Starting from Randomness | Systems of Limited Size and Class 2 Behavior Cyclic multiplication With multiplication by k at each step the dot will be at ...
Notes for: The Crucial Experiment   (Stephen Wolfram's "A New Kind of Science")
(Page 0870d) Notes for: The Crucial Experiment | How Do Simple Programs Behave? More colors [in additive cellular automata] The pictures below show generalizations of rule 90 ...
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