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.
Pseudocode
Run an operation to see its steps.
Avg · Worst
How to use
- 1 Type how many terms (up to 30) and press Build sequence.
- 2 Each new term is the sum of the previous two — watch the two highlighted boxes add up.
- 3 Step back and forward, or use Random.
- 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.
Fibonacci Sequence Visualizer is a free algorithm utility by Zerethon Tools. Animated Fibonacci sequence — each term is the sum of the previous two, built iteratively with step controls. Runs in your browser. Runs entirely in the browser — no signup, no upload.
- Category
- Algorithm
- Pricing
- Free
- Privacy
- Browser-based
- Signup
- Not required
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.
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