Title: collatz fractal extension Post by: M Benesi on January 31, 2014, 08:40:32 AM So, I was looking at the Collatz Problem (http://en.wikipedia.org/wiki/Collatz_conjecture#Collatz_fractal), 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. Title: Re: collatz fractal extension Post by: kram1032 on January 31, 2014, 01:23:56 PM sounds interesting :)
Title: Re: collatz fractal extension Post by: s31415 on January 31, 2014, 05:22:39 PM 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 |