Tuesday, August 29, 2017

Collatz… So what’s the history of it???

I see the always-intriguing Collatz conjecture going around a bit again on Twitter (as it seems to every few months), but just started wondering what the history/background of it is, which I’ve never seen much about, other than that it originated with Lothar Collatz maybe in the 1930s(?).
The simple statement of it, is that you take any positive integer and apply the following 2 rules iteratively:
• If the number is even, divide it by two, or
• If the number is odd, triple it and add one. (Then repeat.)
Doing so successively you will always conclude with a sequence of integers ending at 4, 2, 1 (...or so goes the conjecture).
People write a lot about the conjecture and continue to work on it, but what I’m wondering now is how did Collatz stumble upon those two specific iterative rules to begin with out of essentially an infinite number that might be imagined (even if many would pretty obviously not lead to anything interesting)? Or, you could even come up with 3 iterative rules! Or, or, or… Did he try LOTS of others… have other people since tried LOTS of others? Is there something unique about his two rules, as opposed to ANY others that might be concocted and have some interesting result?
Anyone know, or can point to some informative links?

...And for anyone who's missed it, here's a nice Numberphile introduction to the Collatz conjecture: