"The Intriguing Mathematics Behind the '3n+1' Conjecture"

This is quite a beautiful function.

What is the "3n+1" theorem?

1. Take a random number between 1 to 10.

2. If your number is odd, triple it and add a one (3n+1).

3. If your number is even, divide it by 2

Let's say you took a number, 1. (Good choice!)

1. 3n+1 = 3(1)+1 = 4.

2. n/2 = 4/2 = 2.

3. n/2 = 2/2 = 1. The fact, which is the most astonishing is, take any number between 1 to positive infinity, the number will always jump between: 4, 2, and 1 (in the final three steps)

When this is plotted on a graph, it gives quite a beautiful distribution.

And if you may ask, what is the proof, that it will always end in 4, 2, and 1?

Mathematicians, have solved the "n" until the number of 2^68, and it has always come down to the above three.

The graph due to its unpredictable nature, is also called as "Hailstone-like graph"

or the the famous "Collatz Conjecture")

My take at the conjecture:

Supposing we take, 10(abs(3n+1)) = y

10(abs(n/2)) = y

for any of the absolute value an integer is obtained, its coordinates can be taken as the original "n" and graphed again.

This is, what we get, and I suppose, if we keep doing this, at one point, we get a standard modulus graph, and its coordinates were (-0.4,0.2) which would have been multiplied by 10 to get (-4,2)

as it is limited to positive numbers, we can take 2.

So, the main questions are:-

Is this true for all integers upto infinity?

Is this true for negative numbers/ rational numbers?

How to predict the next highest output of the "3n+1"?

Either way, this is the "3n+1" and thank you for reading ! :)