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

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...

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

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...

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...

Wikimedia Commons has media related to L-systems. Digital morphogenesis Iterated function system Reaction–diffusion system – Type of mathematical model that...

Fractal flames differ from ordinary iterated function systems in three ways: Nonlinear functions are iterated in addition to affine transforms. Log-density...

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...

dynamical system Graph dynamical system Topological dynamical system List of chaotic maps Logistic map Lorenz attractor Lorenz-96 Iterated function system Tetration...

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...

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...

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

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, and...

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...

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

structure. The homeomorphisms may be iterated, resulting in an iterated function system. The composition of functions creates the algebraic structure of...

ISBN 978-0-521-66385-4. Collet, Pierre; Eckmann, Jean-Pierre (1980). Iterated Maps on the Interval as Dynamical Systems. Birkhauser. ISBN 978-0-8176-4926-5. Devaney, Robert...

a short-lived animation studio owned by Hearst Communication. Iterated function system, a method of constructing fractals in mathematics and computer...

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...

zero (in standard Lebesgue measure). Proof: Denote as ai the area of iteration i. Then ai + 1 = ⁠8/9⁠ai. So ai = (⁠8/9⁠)i, which tends to 0 as i goes...

parametric surfaces (e.g., NURBS). Fractals, often defined as an iterated function system. In many vector datasets, each shape can be combined with a set...

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...

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

venue for iteration of systems of functions rather than a single function. For infinite compositions of a single function see Iterated function. For compositions...

Fractal flame Fractal landscape Fractal transform Fractint Graftal Iterated function system Horseshoe map How Long Is the Coast of Britain? Statistical Self-Similarity...

example, solving a linear system of equations A x = b {\displaystyle A\mathbf {x} =\mathbf {b} } by Gaussian elimination). Iterative methods are often the...

an Iterated function system using the set of contraction mappings { d 0 ,   d 1 } {\displaystyle \{d_{0},\ d_{1}\}} . But the result of an iterated function...

{\mathcal {F}}_{n-2}} Lindenmayer system By an iterated construction of 8 square patterns around each square pattern. By an iterated construction of octagons The...

the overlap in a fractal construction. Specifically, given an iterated function system of contractive mappings ψ 1 , … , ψ m {\displaystyle \psi _{1}...

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in...