The Collatz Conjecture is a famous unsolved problem in mathematics which asks if all natural numbers will eventually reach 1 if they are continually passed as arguments to a map f, defined as f(n) = n / 2 if n mod 2 = 0, or f(n) = 3n + 1 if n mod 2 = 1, for n > 0.
There is no complete formal proof of this conjecture, but it is widely believed to be true, even "large" numbers eventually reaching 1 after a series of steps. Unfortunately, my program does not prove the Collatz conjecture, but it does produce a very pretty graph, which you can see below:
You can run Collatz-Grapher just by running some commands like I do below:
Here's what I want to do in the future, if you have any suggestions, feel free to make a PR!
- Application of the collatz map to the input list is an example of an embarassingly parallel problem, I want to leverage parallelism to make this faster. [Complete]
- I want to investigate what causes the bottleneck at around
n ~ 1000000, whether it's due to the limitation of the graphing module, or whether it is due to something else.
In closing, here's a quote about the Collatz conjecture by the famous mathematician Paul Erdos:
"Mathematics may not be ready for such problems"