# All numbers lead to one

Oct 4, 2011

In 1937, mathematician Lothar Collatz proposed that given the following algorithm, you will always end at the number 1:

1. Take any natural number, n.
2. If n is even, divide it by 2.
3. Otherwise, n is odd. Multiply it by 3 and add 1.
4. Repeat indefinitely.

Developer Jason Davies puts it into reverse and shows all the numbers that fall within an orbit length of 18 or less. Press play, and watch the graph grow. Mostly a fun animation for nerds like me.

### 3 Comments

• I love this. I found out about the Collatz conjecture earlier this year and made a tool to explore it in Excel (http://2toria.com/2011/07/01/collatz-conjecture-an-excel-model/).

It’s nowhere near as fancy looking as this though. Great stuff!!

• Jeff Clapper

Love the algorithm. Also, the visualization has a great resemblance to the Death Star.

• jsnumber88

The reason why all these numbers leads to one is because he used 10/10 as his base. Therefore translate to 123 position. equaling to the full calendar days. Interesting algorithm though.