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 2007-07-21, 18:28 #1 nibble4bits     Nov 2005 2·7·13 Posts Related to Collatz conjecture Define a function that can only return integer results, that must always follow the pattern of the next value being 1/3rd, or the next value being 1 plus twice the current value. If x/3 === 0 (mod 3), then x'=x/3 Else x'=2x+1 There are some interesting trees/cycles one can make by changing those coefficients! I'm thinking that there are artist applications of this idea, as well as the purely mathematical. The formula could be generalized as: If (x mod a) == 0, then x' = x/a Else x'=bx+c Each combination of a,b, and c leads to different graphs. Another interesting question has to do with the running fractions based on x/a and bx+c. Is there a method for specific combinations of values, to prove they always stop or at least stop in less steps than the initial x? *Bonus* Extend the formula to the following table for x mod a (start at 0, end at a-1): x/a bx+c dx+e fx+g ... Last fiddled with by nibble4bits on 2007-07-21 at 18:29

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