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...

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...

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...

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...

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...

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...

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 ) )...

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...

Parallel mirrors reflecting each other Iterated function – Result of repeatedly applying a mathematical function Mathematical induction – Form of mathematical...

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...

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

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...

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...

(mathematics) Iterated function List of matrices Nilpotent Pure function Referential transparency This is an equation between functions. Two functions are equal...

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...

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

collective action of a set of contractions, called an iterated function system. The iteration of the operator converges to a unique attractor, which...

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...

of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations...

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...

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

\}}(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...

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...