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Notes for: Systems Based on Numbers | Elementary Arithmetic

*3n+1 problem as cellular automaton

If one writes the digits of n in base 6, then the rule for updating the digit sequence is a cellular automaton with 7 possible colors (color 6 works as an end marker that appears to the left and right of the actual digit sequence):

{a_, b_, c_} -> If[b==6, If[EvenQ[a], 6, 4],
3 Mod[a, 2] + Quotient[b, 2] /. 0 :> 6 /; a == 6]

The 3n+1 problem can then be viewed as a question about the existence of persistent structure in this cellular automaton.


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* Relation [of powers] to substitution systems
* Other uniformly distributed sequences
* Implementation [of 3/2 system]
* The 3n+1 problem
* 3n+1 problem as cellular automaton
* Reconstructing initial conditions [in the 3n+1 problems]
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From Stephen Wolfram: A New Kind of Science [citation] Previous note-----Next note