Recursion is one of the most fundamental concepts of computer science. It is called recursion when a function takes one or more calls to itself during execution. Loop iterations and recursion are different in the sense that loops execute statements repeatedly through a Boolean condition or through a series of elements, whereas recursion repeatedly calls a function. In Python, we can implement a recursive function simply by calling it within its own function body. To stop a recursive function turning into an infinite loop, we need at least one argument that tests for a terminating case to end the recursion. This is sometimes called the base case. It should be pointed out that recursion is different from iteration. Although both involve repetition, iteration loops through a sequence of operations, whereas recursion repeatedly calls a function. Technically, recursion is a special case of iteration known as tail iteration, and it is usually always possible to convert an iterative function to a recursive function and vice versa. The interesting thing about recursive functions is that they are able to describe an infinite object within a finite statement.

The following code should demonstrate the difference between recursion and iteration. Both these functions simply print out numbers between low and high, the first one using iteration and the second using recursion:

Notice that for iterTest, the iteration example, we use a while statement to test for the condition, then call the print method, and finally increment the low value. The recursive example tests for the condition, prints, then calls itself, incrementing the low variable in its argument. In general, iteration is more efficient; however, recursive functions are often easier to understand and write. Recursive functions are also useful for manipulating recursive data structures such as linked lists and trees, as we will see.