In mathematics, an iterated function is a function that is obtained by composing another function with itself two or several times. The process of repeatedly...

In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are...

universe), the iterated logarithm with base 2 has a value no more than 5. Higher bases give smaller iterated logarithms. The iterated logarithm is closely...

iterated exponentials, as it is common to call expressions of this form iterated exponentiation, which is ambiguous, as this can either mean iterated...

can cause drastic changes in the sequence of iterated function values. Thus the behavior of the function on the Fatou set is "regular", while on the Julia...

of statements is said to be iterated; a computer scientist might also refer to that block of statements as an "iteration". Loops constitute the most common...

Fractal image representation may be described mathematically as an iterated function system (IFS). We begin with the representation of a binary image,...

can also be directly iterated over, when the dictionary keys are returned; or the items() method of a dictionary can be iterated over where it yields...

discuss], or rather f = g 1/2 (see Iterated Function), although this leaves the usual ambiguity with taking the function to that power in the multiplicative...

left: The Heighway dragon is also the limit set of the following iterated function system in the complex plane: f 1 ( z ) = ( 1 + i ) z 2 {\displaystyle...

({\boldsymbol {r}}-{\boldsymbol {r}}').} The functional derivative of the iterated function f ( f ( x ) ) {\displaystyle f(f(x))} is given by: δ f ( f ( x ) )...

square root Functional equation Higher-order function Infinite compositions of analytic functions Iterated function Lambda calculus The strict sense is used...

mathematics to investigate the qualitative behaviour of one-dimensional iterated functions, such as the logistic map. The technique was introduced in the 1890s...

sequence x 0 , x 1 , x 2 , … {\displaystyle x_{0},x_{1},x_{2},\dots } of iterated function applications x 0 , f ( x 0 ) , f ( f ( x 0 ) ) , … {\displaystyle...

iterated function. Meyer & Ritchie (1967) showed this correspondence. These considerations concern the recursion depth only. Either way of iterating leads...

the iterated function sequence x, f (x), f (f (x)), f (f (f (x))), ... converges to the fixed point. This concept is very useful for iterated function systems...

This method is also called the chaos game, and is an example of an iterated function system. You can start from any point outside or inside the triangle...

case, the superscript could be considered as denoting a composed or iterated function, but negative superscripts other than − 1 {\displaystyle {-1}} are...

Fractal flames are a member of the iterated function system class of fractals created by Scott Draves in 1992. Draves' open-source code was later ported...

In multivariable calculus, an iterated integral is the result of applying integrals to a function of more than one variable (for example f ( x , y ) {\displaystyle...

reflections that appear to recede to infinity Iterated function – Result of repeatedly applying a mathematical function Mathematical induction – Form of mathematical...

endpoints) is a continuous function whose domain is the unit interval [0, 1]. In the most general form, the range of such a function may lie in an arbitrary...

\}}(s)=\int _{0}^{\infty }e^{-sx}R(x)dx={\frac {1}{s^{2}}}.} Every iterated function of the ramp mapping is itself, as R ( R ( x ) ) = R ( x ) . {\displaystyle...

multi-player iterated version of the game. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's...

attractor, or the fixed point, of any iterated function system (IFS). Starting with any point x0, successive iterations are formed as xk+1 = fr(xk), where...

Idempotent (ring theory) Involution (mathematics) Iterated function List of matrices Nilpotent Pure function Referential transparency "idempotence". Oxford...

of iterated function values. For any function f that maps a finite set S to itself, and any initial value x0 in S, the sequence of iterated function values...

remaining smaller cubes and continue to iterate ad infinitum. The second iteration gives a level 2 sponge, the third iteration gives a level 3 sponge, and so on...

small change in a single variable can have an unpredictable outcome. Iterated function systems (IFS) – use fixed geometric replacement rules; may be stochastic...

In mathematics, the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric, to a given set...