Iterated function information

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...

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

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...

Frederick William Herschel. Repeated composition of such a function with itself is called iterated function. By convention, f 0 is defined as the identity map...

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...

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...

\}}(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 R{\big...

{r}}-{\boldsymbol {r}}').\end{aligned}}} The functional derivative of the iterated function f(f(x)){\displaystyle f(f(x))} is given by: δf(f(x))δf(y)=f′(f(x)...

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...

universe), the iterated logarithm with base 2 has a value no more than 5. Higher bases give smaller iterated logarithms. Indeed, the only function commonly...

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...

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

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...

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...

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

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

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

) } n ∈ N {\displaystyle \{f^{n}(x)\}_{n\in \mathbb {N} }} of the iterated function f {\displaystyle f} . Hence, y ∈ ω ( x , f ) {\displaystyle y\in \omega...

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...

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...

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...

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