Due to the iterative / recursive nature of the technique, complex objects are particularly slow to emulate.

As one illustration, trees, ferns, cells of the nervous system, blood and lung vasculature, and other branching patterns in nature can be modeled on a computer by using recursive algorithms and L-systems techniques.

Act II opens with Vladimir singing a recursive round about a dog, which could illustrate the cyclical nature of the play's universe, and also point toward the play's debt to the carnivalesque, music hall traditions, and vaudeville comedy ( this is only one of a number of canine references and allusions in the play ).

; Deforestation ( data structure fusion ): Because of the high level nature by which data structures are specified in functional languages such as Haskell, it is possible to combine several recursive functions which produce and consume some temporary data structure so that the data is passed directly without wasting time constructing the data structure.

The recursive nature of the L-system rules leads to self-similarity and thereby fractal-like forms are easy to describe with an L-system.

IIR filters, which are by nature recursive have the drawback that if not carefully designed they may enter limit cycles resulting in non-linear distortion.

Because of the algorithm's recursive nature, it can run in real time using only the present input measurements and the previously calculated state ; no additional past information is required.

He sees the brain as a machine that reduces the infinite possibilities of a " quantum-like universal consciousness ", which is a consequence of the " recursive nature of reality ".

It is a recursive process to realize shared goals, ( this is more than the intersection of common goals seen in co-operative ventures, but a deep, collective, determination to reach an identical objective ) — for example, an intriguing endeavor that is creative in nature — by sharing knowledge, learning and building consensus.

Their gradual rehabilitation recently is evident in teleonomy which bears a number of features, such as the description of organisms, that are reminiscent of the Kantian conception of final causes as essentially recursive in nature.

A non-memoized version of the above, given the nature of the recursive algorithm involved, would require n + 1 invocations of to arrive at a result, and each of these invocations, in turn, has an associated cost in the time it takes the function to return the value computed.

Their recent rehabilitation is evident in teleonomy which, bears a number of features, such as the description of organisms, that are reminiscent of the Aristotelian conception of final causes as essentially recursive in nature.

The recursive nature of the law is a reflection of the universal experience of difficulty experienced in estimating complex tasks despite all best efforts, including knowing that the task is complex.

Each System 1 primary activity is itself a viable system due to the recursive nature of systems as described above.

Both Sudan and Ackermann are credited with discovering total computable functions ( termed simply " recursive " in some references ) that are not primitive recursive.

In advanced radiosity simulation, recursive, finite-element algorithms ' bounce ' light back and forth between surfaces in the model, until some recursion limit is reached.

A theory about some topic is usually first-order logic together with: a specified domain of discourse over which the quantified variables range, finitely many functions which map from that domain into it, finitely many predicates defined on that domain, and a recursive set of axioms which are believed to hold for those things.

In fact, it is difficult to devise a computable function that is not primitive recursive, although some are known ( see the section on Limitations below ).

The sub-genre of " recursive science fiction " has a fan-maintained bibliography at the New England Science Fiction Association's website ; some of it is about science fiction fandom, some not.

Predictive parsing is possible only for the class of LL ( k ) grammars, which are the context-free grammars for which there exists some positive integer k that allows a recursive descent parser to decide which production to use by examining only the next k tokens of input.

This indicates that, if f ( n ) is m, then f ( n + 1 ) is ( n + 1 ) m, so that the pair ( n + 1, ( n + 1 ) m ) is in the graph of f. Unlike the base case f ( 0 ) = 1, the recursive operator requires some information about f ( n ) before it defines a value of f ( n + 1 ).

In contemporary use, the term " computable function " has various definitions: according to Cutland ( 1980 ), it is a partial recursive function ( which can be undefined for some inputs ), while according to Soare ( 1987 ) it is a total recursive ( equivalently, general recursive ) function.

These models enable some nonrecursive sets of numbers or languages ( including all recursively enumerable sets of languages ) to be " learned in the limit "; whereas, by definition, only recursive sets of numbers or languages could be identified by a Turing machine.

While the machine will stabilize to the correct answer on any learnable set in some finite time, it can only identify it as correct if it is recursive ; otherwise, the correctness is established only by running the machine forever and noting that it never revises its answer.

Stack overflow may be difficult to avoid when using recursive procedures, since many compilers assume that the recursion stack is a contiguous area of memory, and some allocate a fixed amount of space for it.

In such cases, supposing that the chain of primes extended all the way down to some bounded value, the recursive application of Rader's algorithm would actually require O ( N < sup > 2 </ sup >) time.

Many compilers can also inline expand some recursive functions ; recursive macros are typically illegal.

Some authors use the transpose of this matrix, which ( dually ) cycles coordinates, and is more convenient for some purposes, like linear recursive relations.

# Composition: applying values from some elementary recursive function as an argument to another elementary recursive function.

A recursive definition of a function defines values of the functions for some inputs in terms of the values of the same function for other inputs.

The " regular expressions " in current versions of AWK and Perl are in fact extensions of regular expressions in the traditional sense, but regular expressions, unlike SNOBOL4 patterns, cannot be recursive, which gives a distinct computational advantage to SNOBOL4 patterns.

The recursion in patterns in this example are trivial, but a possible more complex recursive pattern would be something like < tt > Node ( Node ( Leaf 4 ) x ) ( Node y ( Node Empty z ))</ tt >.

This task may seem easy for the simple patterns above, but with many complicated recursive patterns, the task becomes difficult for the average human ( or compiler, if it has to check arbitrary nested if-else constructs ) to handle.

The set of equations ( 5 ), ( 6 ), and the starting equation ( 7 ) is of a recursive type well suited to programming on the digital computer.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.

However, the recursion is bounded because in each recursive application either m decreases, or m remains the same and n decreases.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

This extreme growth can be exploited to show that f, which is obviously computable on a machine with infinite memory such as a Turing machine and so is a computable function, grows faster than any primitive recursive function and is therefore not primitive recursive.

Seed AI is a hypothesized type of strong artificial intelligence capable of recursive self-improvement.

A common adaptive method is recursive subdivision, in which a curve's control points are checked to see if the curve approximates a line segment to within a small tolerance.

The recursive equation is best introduced in a slightly more general form

Although the above recursive formula can be used for computation it is

It is not feasible to carry out such a computation using the above recursive formulae, since at least ( a constant multiple of ) p < sup > 2 </ sup > arithmetic operations would be required.

Note that this is different from the recursive languages which can be decided by an always-halting Turing machine.

Note that the set of grammars corresponding to recursive languages is not a member of this hierarchy.

Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.