Skip to main content
Z

Fibonacci Visualizer — Build the Sequence

Animated Fibonacci sequence — each term is the sum of the previous two, built iteratively with step controls. Runs in your browser.

Free No signup Client-side Privacy friendly Updated

/

Pseudocode

Run an operation to see its steps.

How to use

  1. 1 Type how many terms (up to 30) and press Build sequence.
  2. 2 Each new term is the sum of the previous two — watch the two highlighted boxes add up.
  3. 3 Step back and forward, or use Random.
  4. 4 The sequence starts F(0) = 0, F(1) = 1.

Why use this tool

  • See the Fibonacci sequence built iteratively in O(n) — no slow recursion.
  • Watch each term form from the sum of the two before it.
  • Understand why the iterative approach beats naïve recursion’s exponential time.
  • Runs entirely in your browser. No signup, no uploads.

Frequently asked questions

What is the Fibonacci sequence?

A sequence where each number is the sum of the two preceding ones, starting 0, 1, 1, 2, 3, 5, 8, 13, 21, … It appears throughout mathematics and nature.

What is the time complexity of computing Fibonacci numbers?

The iterative method shown here is O(n) time and O(1) space. Naïve recursion is O(2ⁿ); memoized recursion (dynamic programming) is O(n).

Why is naïve recursive Fibonacci so slow?

It recomputes the same subproblems exponentially many times. Memoization or the iterative loop computes each term once, turning O(2ⁿ) into O(n).

What is the golden ratio’s connection?

The ratio of consecutive Fibonacci numbers F(n+1)/F(n) approaches the golden ratio φ ≈ 1.618 as n grows.

What is Fibonacci Sequence Visualizer?

A Fibonacci Sequence Visualizer builds the sequence iteratively, where each term F(i) = F(i-1) + F(i-2) starting from F(0)=0 and F(1)=1. It highlights the two terms being summed and the new term, in O(n) time.

Features

Step-by-step animation

Watch terms build up, and see the recursion tree's repeated subproblems.

Complexity

Naive recursion: O(φⁿ) exponential. Iterative / memoized: O(n) time, O(1) space.

100% private

Runs entirely in your browser — nothing is uploaded.

Example

Input

first 7 terms

Output

0, 1, 1, 2, 3, 5, 8   (F(6) = 8)

Common use cases

  1. 1

    Motivate memoization

    See why the recursion tree recomputes subproblems and how DP fixes it.

  2. 2

    Learn the sequence

    Understand the additive rule and its link to the golden ratio.

  3. 3

    Recursion vs iteration

    Compare exponential recursion against linear iteration.

Summary

Zerethon's Fibonacci visualizer animates how each term is the sum of the previous two (0, 1, 1, 2, 3, 5, 8, …) in your browser, illustrating both the exponential naive recursion and the linear iterative/memoized approach. Naive recursion is O(φⁿ) (≈ O(1.618ⁿ)); the iterative method is O(n) time and O(1) space.

Category
Algorithm
Pricing
Free
Privacy
Browser-based
Signup
Not required

References

Privacy

Your data never leaves your browser unless explicitly stated. Fibonacci Sequence 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 Dynamic Programming →

Related tools

Bubble Sort Visualizer

Animated bubble sort with step controls, speed, custom input, live comparison/swap counters and pseudocode. Runs entirely in your browser.

Open tool

Insertion Sort Visualizer

Animated insertion sort with step controls, speed, custom input, live comparison/write counters and pseudocode. Runs in your browser.

Open tool

Selection Sort Visualizer

Animated selection sort with step controls, speed, custom input, live comparison/swap counters and pseudocode. Runs in your browser.

Open tool

Merge Sort Visualizer

Animated merge sort with step controls, speed, custom input, live comparison/write counters and pseudocode. Runs in your browser.

Open tool

Build, share, and grow on Zerethon Social

Free signup. Earn points, collect achievements, and connect with creators worldwide.

Try Zerethon free