![]() ![]() For example, the formal definition of the natural numbers by the Peano axioms can be described as: "Zero is a natural number, and each natural number has a successor, which is also a natural number." By this base case and recursive rule, one can generate the set of all natural numbers. Many mathematical axioms are based upon recursive rules. The Fibonacci sequence is another classic example of recursion:įib(0) = 0 as base case 1, Fib(1) = 1 as base case 2, For all integers n > 1, Fib( n) = Fib( n − 1) + Fib( n − 2). One's parent's ancestor ( recursive step).A recursive step - a set of rules that reduces all successive cases toward the base case.įor example, the following is a recursive definition of a person's ancestor.A simple base case (or cases) - a terminating scenario that does not use recursion to produce an answer. ![]() In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: ![]() While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references can occur.Ī process that exhibits recursion is recursive.įormal definitions Ouroboros, an ancient symbol depicting a serpent or dragon eating its own tail The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. Recursion is used in a variety of disciplines ranging from linguistics to logic. Recursion occurs when the definition of a concept or process depends on a simpler version of itself. 1904 Droste cocoa tin, designed by Jan Misset The woman in this image holds an object that contains a smaller image of her holding an identical object, which in turn contains a smaller image of herself holding an identical object, and so forth. For other uses, see Recursion (disambiguation).Ī visual form of recursion known as the Droste effect. ![]()
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