Notes

Chapter 4: Systems Based on Numbers


Section 2: Elementary Arithmetic

3n+1 problem as cellular automaton A reversible [3n+1 problem] system Digit count sequences Digit counts Digit reversal General powers [of numbers] History [of reversal-addition systems] Implementation [of 3/2 system] Iterated bitwise operations Iterated run-length encoding Leading digits [in numbers] Multiples of irrational numbers Multiplicative digit sequences Negative bases Non-power bases Other uniformly distributed sequences Powers of 3/2 Powers of three in base 2 Reconstructing initial conditions [in the 3n+1 problems] Relation [of powers] to substitution systems Reversal-addition systems Substitution systems [and digit sequences] The 3n+1 problem

From Stephen Wolfram: A New Kind of Science [citation]