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Collatz Conjecture Visualizer — 3n+1 Sequence

Animated Collatz (3n+1) sequence as a line chart — watch the trajectory climb and fall to 1. Step controls. Runs in your browser.

Free No signup Client-side Privacy friendly Updated

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Pseudocode

Run an operation to see its steps.

How to use

  1. 1 Type a starting number and press Run sequence.
  2. 2 At each step: if the number is even, halve it; if odd, triple it and add one.
  3. 3 Watch the trajectory until it reaches 1.
  4. 4 Try 27 for a famously long, spiky path, or use Random.

Why use this tool

  • See the surprising up-and-down trajectories the Collatz rule produces.
  • Watch even/odd steps and the peak value before the sequence collapses to 1.
  • Explore an unsolved problem — no counterexample has ever been found.
  • Runs entirely in your browser. No signup, no uploads.

Frequently asked questions

What is the Collatz conjecture?

Start with any positive integer. If it is even, divide by 2; if odd, compute 3n+1. The conjecture states that this process always eventually reaches 1, no matter the starting number.

Is the Collatz conjecture proven?

No. It remains unproven despite enormous effort, though it has been verified by computer for every starting value up to astronomically large numbers.

Why is the number 27 interesting?

Starting from 27 the sequence takes 111 steps and climbs as high as 9232 before finally descending to 1 — surprisingly dramatic for such a small start.

What are these numbers called?

The sequence of values is the Collatz (or 3n+1) trajectory, and the number of steps to reach 1 is its total stopping time.

What is Collatz Conjecture Visualizer?

A Collatz Conjecture Visualizer plots the 3n+1 sequence: from a starting number it halves even values and computes 3n+1 for odd values, charting the trajectory until it reaches 1. The conjecture that every start reaches 1 remains unproven.

Features

Step-by-step animation

Watch the sequence rise and fall until it collapses to 1.

Honest status

The conjecture is unproven; sequence length has no known formula.

100% private

Runs entirely in your browser — nothing is uploaded.

Example

Input

start 6

Output

6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1 (8 steps)

Common use cases

  1. 1

    Explore the conjecture

    Try starting values and watch their trajectories to 1.

  2. 2

    See chaotic behavior

    Observe how nearby starts can take very different paths.

  3. 3

    Learn an open problem

    Understand a famous unsolved problem in mathematics.

Summary

Zerethon's Collatz conjecture visualizer animates the 3n+1 sequence in your browser: from any positive integer, halve it if even or triple-plus-one if odd, and repeat. The Collatz conjecture states every starting value eventually reaches 1 — verified for enormous ranges but still unproven. Sequence length varies unpredictably, so no closed-form running time is known.

Category
Algorithm
Pricing
Free
Privacy
Browser-based
Signup
Not required

References

Privacy

Your data never leaves your browser unless explicitly stated. Collatz Conjecture Visualizer runs entirely client-side — no server upload, no logging, no tracking of your input.

New to this? Read the step-by-step explanation with Big-O analysis: Learn Number Theory →

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