What is recursion?
Simply defined, a recursive function is one that calls itself. While that definition may be simple, writing a recursive function for the first time can be difficult because it requires a different method of thinking.

Most functions are coded in a fairly straightforward fashion -- you progress from point A, to point B, and end at point C. You may have loops and If Then statements, but you can easily visualize the function in a linear fashion. Recursive functions, however, take an inside-out approach to arriving at an answer. Consider the recursive function below, which calculates the factorial of a number. The factorial of a number is arrived at by multiplying it by all smaller integers. So, the factorial of 3 (denoted as 3!) is equal to 3 * 2 * 1, or 6.

Function factorial (i as integer) as long If i = 1 then Factorial = 1 Else Factorial = i * Factorial(i -1) End If End Function

Stepping through a recursive function
Let's step through this function to see how recursion works. We'll assume that you've called the factorial function with a value of 3 as the integer parameter.

You can easily see that since 3 is not equal to 1, the line of code you're concerned with here is:

Factorial = i * Factorial(i - 1)

In English, this line would roughly translate into "The factorial of 3 is equal to 3 times the factorial of 2." So, in other words, the factorial of 3 is equal to 3 times some as of yet unknown value.

Let's figure out that unknown value. If you were to call the factorial function with a value of 2 (which is exactly what this function is doing), you'd see that the factorial of 2 is equal to 2 times the factorial of 1.

You're almost there! Call the factorial function with a value of 1, and the answer is simple: The factorial of 1 is 1. Now what?

Let's take a look at the results we've come up with so far:

3! = 3 * 2! 2! = 2 * 1! 1! = 1

Working from the bottom up, you can easily see that the factorial of 3, or 3!, is equal to 6.