I am working on a program that does some stuff with the collatz conjecture. I originally wrote it in Python as that is the language I am most familiar with:

n = []
mod = []
step = 0

def lstfill(nb,ne,lst):
    while nb <= ne:

def collatz(n, s):
    for i in n:
        s = 0
        print "starting #", i
        while i != 1:
            if i%2==0:
                print i
                print i
        print "mod:", mod
        print "steps:", s

collatz(n, step)

However, there are some things I need to do that I can't really do without downloading libraries and I can't do that. So I thought I'd switch to Mathematica. Except I looked at my code and realized I had no idea how to write this code in the Mathematica language. How would I manipulate lists, or create functions, or anything like that? And what is the equivalent of the modulo operator?

Any help would be appreciated. Thanks!

  • $\begingroup$ Did you look up Mod[] already? Have you also searched the site for "collatz"? $\endgroup$ – J. M.'s ennui Oct 13 '16 at 1:54
  • $\begingroup$ @J.M., thank you for the Mod[] command! I guess I kind of wanted to be able to use my own code that I wrote in Python, just translate it, and I didn't know quite how to write a function or manipulate lists. $\endgroup$ – heather Oct 13 '16 at 1:57
  • $\begingroup$ Btw, for this application you can - and should - easily add memoization. Simulation of Collatz over a set of initial conditions will inevitably overlap previous computed values. $\endgroup$ – alancalvitti Oct 13 '16 at 4:18

This question demonstrates one of the best things I love about Mathematica; mathematical notation as code.

Using Esc+pw+Esc and Ctrl+Enter you can enter the function in Piecewise mathematical notation.

Mathematica graphics

or by code

f[n_Integer] := Piecewise[{{n/2, Mod[n, 2] == 0}, {3*n + 1, Mod[n, 2] == 1}}]

Then with NestWhileList and the Pure Function # != 1 & for stopping,

NestWhileList[f, 8, # != 1 &]
{8, 4, 2, 1}

and with an odd number start,

NestWhileList[f, 11, # != 1 &]
{11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1}

I much prefer these two lines of code to the alternative.

Hope this helps.

  • $\begingroup$ It's what I like about Mathematica too: you can often say a lot with much less. :) $\endgroup$ – J. M.'s ennui Oct 13 '16 at 2:26
  • $\begingroup$ @heather You can use f[n_Integer/;Positive[n]] to be more strict on the the integers f will accept. I left that out for simplicity as you are just starting. $\endgroup$ – Edmund Oct 13 '16 at 2:33
  • $\begingroup$ I would've done that as f[n_Integer?Positive] myself. ;) $\endgroup$ – J. M.'s ennui Oct 13 '16 at 2:59
  • $\begingroup$ Wow, thanks! I didn't realize how much shorter the Mathematica code would be. =) I'm now working on expanding the code and I think I get the general-ish idea of the functions and while loops, so thank you very much! $\endgroup$ – heather Oct 13 '16 at 11:22
  • $\begingroup$ to be fair, the python version could be made a lot shorter too. $\endgroup$ – george2079 Oct 13 '16 at 21:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.