[pdx.st] Meeting tonight!

markus markus at reality.com
Tue Jul 29 16:58:25 PDT 2014


> Hey, catapults, trebuchets... interesting stuff!  Perhaps you're 
> interested in this as well?
> 
> http://www.meetup.com/Relativity-Exploration-of-Portland/events/195756892/?_af_eid=195756892&_af=event&a=uc1_vm

Argh, another interesting thing I'll have to miss (in this case, because
I'll be presenting at pdx rb)!

The Math Club kids spent a few weeks on 3x+1 and closely related
problems last fall.  It's a wonderful area to explore, with lots of
interesting nooks and crannies.  Some that I recall they had fun with:

      * What does it look like mod 6, mod 18, and in general in mod
        2^x*3^y
      * What bounds can you set on the smallest y that will lead to a
        given x?  y<=2*x is immediate, but can you do better?
      * If we call f(x) = even(x) ? x/2 : 3x+1, and g(x) = f(f(x)), what
        do we see?  Likewise for h(x) = f(f(f(x))) and so forth.
      * Can we find anything like mandlebrot in the convergence times?
      * If some x doesn't dominate 1, it must either grow without bound
        or be part of some cycle which does not include 1.  Can we say
        anything about these possibilities?

And it looks like you've found a whole slew of similarly interesting
questions to ask about it.

Hope you get to feeling better soon!

-- M






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