What is "recursion"

Recursion \Re*cur"sion\ (-sh?n), n. [L. recursio. See Recur.]

1. The act of recurring; return. [Obs.]
   --Boyle.

2. (Math.) The calculation of a mathematical expression (or a quantity) by repeating an operation on another expression which was derived by application of the same operation, on an expression which itself was the result of similar repeated applications of that same operation on prior results. The series of operations is terminated by specifying an initial or terminal condition.

3. (Computers) A programming technique in which a function calls itself as a subfunction. Such calls may be repeated in series to arbitrary depth, provided that a terminating condition is given so that the final (deepest) call will return a value (rather than continue to recurse), which then permits the next higher call to return a value, and so forth, until the original call returns a value to the calling program.

1610s, from Latin recursionem (nominative recursio) "a running backward, return," noun of action from past participle stem of recurrere "run back" (see recur).

n. 1 The act of recurring. 2 (context mathematics English) The act of defining an object (usually a function) in terms of that object itself. 3 (context computing English) The calling of a function from within that same function.

n. (mathematics) an expression such that each term is generated by repeating a particular mathematical operation

Recursion occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no loop or infinite chain of references can occur.

The term is also used more generally to describe a process of repeating objects in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other, the nested images that occur are a form of infinite recursion.

Recursion (2004) is Tony Ballantyne's first novel. It is in the science fiction genre and follows three separate characters and their stories in a futuristic dystopia.

Of high import to the storyline is the concept of the Singularity, a point in the near future when the evolution of technology reaches such a speed that thinking machines outpace human minds, a point beyond which we cannot possibly predict what will happen; and that of von Neumann machines, self-replicating robots that use available raw resources to make copies of themselves. The implication is that a system of such machines (just one would suffice) that is allowed to reproduce unchecked will in short order devour entire biospheres, perhaps even entire solar systems or galaxies if these von Neumann machines are equipped with propulsion devices. An interesting corollary to this is that if two systems of von Neumann machines are battling for resources, the winner will not be decided by which group has the most members; the victorious system will be the one that reproduces faster. Also brought up by Ballantyne is the intriguing possibility of being copied and inserted into a simulation. Bostrom's tripartition tends to suggest that we ourselves are living in a simulated universe. Moments exist in Recursion' in which the main character is rather unsure if he is in reality or a simulation — certain bugs in the program make themselves apparent, such as blank spaces appearing between buildings and the ground, causing him to question reality. Eventually it becomes apparent that he has been copied multiple times, and inserted into various simulations, and that what he thinks of as his identity is truly not the original, but merely one of many copies. It can be argued, however, that perfect copies, at the moment of creation, are identical and indistinguishable from their originals. A copy is the original, so to speak.

Category:2004 British novels Category:2000s science fiction novels Category:British science fiction novels Category:Debut novels Category:Dystopian novels

Recursion in computer science is a method where the solution to a problem depends on solutions to smaller instances of the same problem (as opposed to iteration). The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science.

"The power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite statement. In the same manner, an infinite number of computations can be described by a finite recursive program, even if this program contains no explicit repetitions."

Most computer programming languages support recursion by allowing a function to call itself within the program text. Some functional programming languages do not define any looping constructs but rely solely on recursion to repeatedly call code. Computability theory proves that these recursive-only languages are Turing complete; they are as computationally powerful as Turing complete imperative languages, meaning they can solve the same kinds of problems as imperative languages even without iterative control structures such as “while” and “for”.

Recursion is the process of repeating items in a self-similar way.

Recursion may also refer to

• Mathematical induction, a method of proof also called "proof by recursion"
• Recursion (computer science), a method where the solution to a problem depends on solutions to smaller instances of the same problem
• Recurrence relation, a recursive formula for a sequence of numbers a
• Recursion (novel) (2004), a science fiction novel by Tony Ballantyne
• Nyaya (Sanskrit, literally "recursion"), the Hindu philosophical school of logic
• Recursive science fiction, science fiction about science fiction