What does recursion mean?
Recursion is the process of applying a rule repeatedly, with the result of one step becoming the input to the next. In mathematics, it describes a definition that refers back to itself, usually while moving toward a base case that stops the process. In computer science, recursion means that a function calls itself, either directly or through other functions, to solve a problem. The word also applies more broadly to self-reference and repeated patterns in language, art, philosophy, and other fields. Recursion is useful because it expresses processes that naturally contain smaller versions of themselves, although careless use can lead to infinite repetition or stack exhaustion. The concept appears in mathematical induction, recursive grammatical rules, fractal-like imagery, and self-referential philosophical arguments.
nounRecursion is the process of repeating a sequence of steps or applying a rule to a result that is itself subject to the same rule. In mathematics and computer science, it often refers to a definition or procedure that refers back to itself.
- The repeated application of a rule or procedure, with each result potentially producing another application of the same rule.
- In mathematics, a definition or proof that refers to itself, usually through a well-founded process that eventually reaches a base case.
- In computer science, a function or procedure that invokes itself, directly or indirectly, to solve a problem.
- The general phenomenon of a process returning to an earlier state, structure, or point of reference.
"The recursive function calls itself until it reaches its base case."
"The recursive procedure calls the function again with a smaller input."
"The critic found a paradox in the sentence because its meaning depends on a form of linguistic recursion."
"The artist used recursion to create a pattern that repeatedly reproduces smaller versions of itself."
The plural is used when referring to multiple recursive processes, definitions, or examples.
"The two recursions in the program produce different results because their base cases differ."
Recursion is the mathematical idea of a definition that contains the definition it is trying to explain.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does recursion come from?
The English noun comes from Latin recursio, a noun formation meaning a running back or return, derived from recurrere, “to run back.” Latin recurrere was formed from re-, meaning “back,” and currere, meaning “to run.” The word was established in English mathematical and philosophical usage and later became especially important in computer science.
Related word forms
How recursion is actually used
The term is most common in mathematics, computer science, linguistics, and philosophy. In computing, recursion is often contrasted with iteration; both express repetition, but recursion specifically involves a procedure or definition referring back to itself. It can also describe any deliberately self-similar artistic or cultural pattern.
Easily confused with recursion
A recurrence is an instance of something happening again, whereas recursion is the process or structure by which repetition or self-reference is defined.