Recursion refers to when a data structure contains simpler versions of itself within it. One can move up and down the stack of levels, by popping, or pushing, respectively.
An example of such a recursive stack is the Call stack
Recursion in mathematics
Recursion in computer science
See Programming, Algorithms
Recursion in Music
Bach - LITTLE HARMONIC LABYRINTH - BWV 591
Recursion in Language
Recursive transition networks, or Railroad diagrams are use to express Context-free grammars.
Recursions can give rise to things that are defined in terms of themselves, but still not being paradoxical! The reason they avoid self-reference, is because there should be a part of the definition which avoids self-reference. This is the terminating condition in standard recursive functions.
Recursion can also be indirect when two or more functions call each other, in a loop. Heterarchy
Combinatorial structures are often analyzed using recursive definitions in Analytic combinatorics.
bounded, and free loops.
Augmented transition networks.