The Collatz conjecture's rules are very easy:

if this number is odd, multiply it by three and then add one to it
if this number is even, divide it by 2
if this number becomes 1 after repeating rule 1 and two,congrats,
just proved the number you started with follows the conjecture!

13-40-20-10-5-16-8-4-2-1

33-100-50-25-76-38-19-58-29-88-44-22-11-34-17-52-26-13

Whoa! That was a long one!But as soon as it reaches 13,
we already proved it because after it gets to 13,
it does what the first example does.

With this figured out, we can also prove that
100,50,25,76.....(all the numbers between)can follow the conjecture too!

For having a better look at this conjecture, I wrote a PYTHON program

The variable 'a' refers to the number in the start

You can see how the numbers slides back to 1

For example: You can see 33:

And you can see many numbers go up high,like 1000:

Or some number falls quickly, like 10000:

And 27, this little number can rise up to above 8000! It's graph is quite like 1000's:

Quite fun, isn't it? Here are some sources to make you know more!

The Collatz Conjecture