Collatz Conjecture Visualiser
Explore the Collatz conjecture — a simple rule with a famously unsolved mystery.
A simple rule, an unsolved puzzle
The Collatz conjecture starts from any number and applies a simple rule repeatedly: if even, halve it; if odd, triple it and add one. The conjecture is that every starting number eventually reaches one. This visualises the sequence for any number you pick.
Enter a number to see its Collatz sequence.
Why this simple problem is famous
The Collatz conjecture is celebrated because it is astonishingly simple to state — a child can understand the rule — yet no one has been able to prove it is always true, despite enormous effort, making it one of the most famous unsolved problems in mathematics. The sequences themselves are wonderfully erratic: some numbers reach one quickly, others soar to surprising heights and take many steps, wandering up and down with no obvious pattern before finally crashing to one. Every number ever tested does reach one, but tested is not proved, and a proof has resisted the field's best minds for decades. Watching the wild, unpredictable paths different starting numbers take is a vivid reminder that simplicity and difficulty are very different things in mathematics, and that mystery can hide inside the most elementary-looking rules.
Questions & answers
What is the Collatz rule?
Start with any number: if it is even, halve it; if odd, triple it and add one. Repeat. The conjecture is that you always eventually reach one.
Why is it famous?
Because it is trivial to state yet unproven despite decades of effort — every tested number reaches one, but no one has proved it always must.
Is anything uploaded?
No. The visualisation happens in your browser.