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Re: Re: Faster alternative to AppendTo? --

• To: mathgroup at smc.vnet.net
• Subject: [mg102974] Re: [mg102942] Re: [mg102886] Faster alternative to AppendTo? --
• From: "Elton Kurt TeKolste" <tekolste at fastmail.us>
• Date: Thu, 3 Sep 2009 05:41:58 -0400 (EDT)
• References: <200909010753.DAA18801@smc.vnet.net>

This will not work as 1 is not a fixed point unless you make it so: 

collatz[1]:=1

On Wed, 02 Sep 2009 04:07 -0400, "Kurt" <ekt at fastmail.net> wrote:
> Try this (you're on your own for timing long runs)
> 
> collatz[x_Integer/;EvenQ[x]]:=x/2
> collatz[x_Integer]:=3 x +1
> 
> Then the orbit of an integer n is given by
> 
> FixedPointList[collatz,n]
> 
> If you'd like to be cautious and put a limit on the calculation, you may
> with
> 
> FixedPointList[collatz, n, limit]
> 
> Of course you can restart the investigation by using the last entry in
> the list for n as n in a new calculation.
> 
> Kurt
> 
> 
> On Tue, 01 Sep 2009 03:53 -0400, "Dem_z" <dem_z at hotmail.com> wrote:
> > Hey, sorry I'm really new. I only started using mathematica recently, so
> > I'm not that savvy.
> > 
> > Anyways, I wrote some code to calculate (and store) the orbits around
> > numbers in the Collatz conjecture.
> > 
> > "Take any whole number n greater than 0. If n is even, we halve it (n/2),
> > else we do "triple plus one" and get 3n+1. The conjecture is that for all
> > numbers this process converges to 1. "
> >  http://en.wikipedia.org/wiki/Collatz_conjecture
> > 
> > 
> > (*If there's no remainder, divides by 2, else multiply by 3 add 1*)
> > g[n_] := If[Mod[n, 2] == 0, n/2, 3 n + 1]
> > 
> > (*creates an empty list a. Loops and appends the k's orbit into variable
> > "orbit", which then appends to variable "a" after the While loop is
> > completed.  New m, sets new k, which restarts the While loop again.*)
> > a = {};
> > Do[
> >   k = m;
> >   orbit = {k};
> >   While[k > 1, AppendTo[orbit, k = g[k]]];
> >   AppendTo[a, orbit];
> >   , {m, 2,1000000}];
> > 
> > Anyways it seems that the AppendTo function gets exponentially slower, as
> > you throw more data into it. Is there a way to make this more efficient?
> > To calculate a million points takes days with this method.
> > 
> -- 
>   Love,
>   Kurt
>   ekt at fastmail.net
> 
> 
Regards,
Kurt Tekolste

• References:
  • Faster alternative to AppendTo?
    • From: Dem_z <dem_z@hotmail.com>