collatz fractal extension

[M Benesi]

So, I was looking at the Collatz Problem, and saw that it works for all primes.

  The basic is :  if mod 2=0; divide x by 2
  else 3 *x +1

  Well, You can extend the primes.  In other words:

  if mod 2=0, divide x by 2.
  if mod 3=0, divide x by 3.

  else  x* 5 +1       (5 being the next prime)

  It works for all primes, so should make a nice mandy type 3d- something grainlier than what we've got so far.
  

 I'm hammered, and about to embark on a journey, so I hope some of you guys take care of business.

  Benesi.

[kram1032]

sounds interesting 

[s31415]

I remembered I heard of this problem back in the 90's and did some (lost) experiments. There is a neat way of extracting some kind of a fractal out of it. Simply plot the number n of iterations it takes you to get to 1, as a function of the starting number x. (Like draw a vertical bar of height n above the point at x on the horizontal axis.) For some reason the bars are not distributed randomly, but tend to be aligned in something vagely reminiscent of a fractal pattern.

See for instance this link for some pictures:
http://protempore.net/~calvins/misc/collatz/

[Edit:] I had missed the wikipedia link, which displays a somewhat similar picture...

Sam