Enter a number and click “Run Collatz” to see step-by-step reasoning here. (Try spamming a large number)
What is happening?
This tool follows a simple mathematical rule called the Collatz Conjecture.
The rule is:
- Choose a number
- If a number is even → divide it by 2
- If a number is odd → multiply by 3 and add 1
- Repeas step 2 and 3 untill you reach 1.
You repeat this process over and over with each new number.
Why this is interesting
Even though the rule is simple, the sequence behaves in a chaotic way:
- Numbers can go up and down unpredictably
- Some numbers grow very large before shrinking
- But they always seem to eventually reach 1
Once it reaches 1, it enters a loop:
1 → 4 → 2 → 1 → ...
What this program shows you
This tool does 3 things:
- Shows every number in the sequence
- Explains each step as it happens
- Counts how many steps it takes to reach 1
Mathematicians still don’t know why this always works for every number — even though it has been tested for billions of cases.