JavaScript Recursion: Fibonacci Sequence

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The Fibonacci sequence is one of those mathematical wonders that seems to pop up everywhere, from the branching of trees to the spiral of a galaxy. It's also a favorite among programmers as it provides a great opportunity to flex our recursive muscles. So, let's dive into the world of JavaScript and see how we can implement this fascinating sequence using recursive functions.

Recursive Functions

Recursive functions are functions that call themselves within their own definition. This may sound like a circular argument that could go on forever, but fear not, we can ensure that our function doesn't become the coding equivalent of a dog chasing its own tail by using a condition to halt the recursion. This is known as a base case.

For a quick introduction on recursion, you can check out this article.

Fibonacci Sequence

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. The beginning of the sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

Now, let's implement this in JavaScript using recursion.

function fibonacci(n) {
    if (n <= 1) {
        return n;
    } else {
        return fibonacci(n - 1) + fibonacci(n - 2);
    }
}
console.log(fibonacci(10));  // Output: 55

In this code, the base case is when n <= 1. In these cases, the function simply returns n. For any larger values of n, the function calls itself twice – once with the argument n - 1 and once with n - 2 – and adds these two values together. This corresponds exactly to the definition of the Fibonacci sequence!

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