Collatz Orbits
The Collatz conjecture is the simplest unsolved problem in mathematics: take any positive integer, halve it if even or triple-plus-one if odd, and repeat; it always seems to reach 1, but no one has proved it must. This tool shows the conjecture two ways. Enter a number and watch its hailstone sequence bounce up and down before crashing to 1, plotted as it goes. Or grow the Collatz tree: draw the path of every number as a line that turns one way on an even step and the other on an odd step, and thousands of overlaid paths bloom into an organic, coral-like or tree-like structure.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- The rule is n → n/2 when even, n → 3n+1 when odd; sequences can soar far above the starting number (27 climbs past 9000) before eventually falling to 1.
- Every number tested — into the quintillions — reaches 1, yet there is no proof it always does, which is why the conjecture remains open.
- Drawing each step as a small turn turns the boring number sequences into a branching plant: shared tails of the sequences overlap into a trunk, and the many paths fan out as branches.
- Runs 100% in your browser — simulations are computed locally on your device.
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