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...

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...

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...

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...

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...

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...

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

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

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...

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...

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

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...

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...

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

computer-assisted composition, and in particular iterated function systems music, in which a function "is applied repeatedly, each time taking as argument...

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...

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...

{\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...

mathematical functions. Each function is a composition of an affine map, and usually some non-linear map. This set of functions is called an iterated function system...