ProofAtlas

Interactive mathematics

Explore mathematics

Start with Collatz: change a starting number, compare examples, and see what happens.

Number theory

Collatz Explorer

Start with a positive whole number. If it is even, halve it. If it is odd, multiply it by 3 and add 1. Repeat, stopping if you reach 1.

Follow a Collatz trajectory, compare starting numbers, and see where their paths meet.

Open Collatz Explorer
110010,0000111 steps
Starting at 27 · 111 steps to 1 · logarithmic height

Choose a starting question

What happens to 27?

Follow one number through its rises and falls.

Try this example

Where do 27 and 28 meet?

Compare two neighbors with very different journeys.

Try this example

How do 128 paths connect?

See the shared branches for starting numbers 1–128.

Try this example

The Collatz conjecture asks whether every positive whole number eventually reaches 1. Checking these examples does not settle the conjecture.