Brenton Bostick
Wittenberg University
Springfield, OH
Registered: Oct 2003
Posts: 1 
On Two Mechanisms Related To The 3n+1 Problem
I have submitted a paper entitled "On Two Mechanisms Related To The 3n+1 Problem" to the MCURCSM conference at Denison University.
Abstract: Let T(n) = (3n+1)/2 if n odd, and n/2 if n even. The 3n+1 problem asks if for all integers n >= 1, there exists an i such that T^i(n) = 1. In this paper, I present two mechanisms related to the problem. The first is a cellular automaton that computes iterations of the 3n+1 function. The second is a function that computes successive local maxima and minima of the sequence generated by iterating T.
The conference website is http://www.denison.edu/mathsci/mcurcsm2003/index.html
The 3n+1 problem is a perfect problem to look at when talking about complex behavior from simple rules. Even though the function is simply defined, the resulting behavior (the number of iterations required for each integer to go to 1) is chaotic and random looking.
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