Sierpinski triangle created using IFS (colored to illustrate self-similar structure)Colored IFS designed using Apophysis software and rendered by the Electric Sheep.
In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry.[1] They were introduced in 1981.
IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system"). The canonical example is the Sierpiński triangle. The functions are normally contractive, which means they bring points closer together and make shapes smaller. Hence, the shape of an IFS fractal is made up of several possibly-overlapping smaller copies of itself, each of which is also made up of copies of itself, ad infinitum. This is the source of its self-similar fractal nature.
^Zobrist, George Winston; Chaman Sabharwal (1992). Progress in Computer Graphics: Volume 1. Intellect Books. p. 135. ISBN 9780893916510. Retrieved 7 May 2017.
and 22 Related for: Iterated function system information
In mathematics, iteratedfunctionsystems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are...
In mathematics, an iteratedfunction 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 iteratedfunctionsystem (IFS). We begin with the representation of a binary image, where...
can cause drastic changes in the sequence of iteratedfunction values. Thus the behavior of the function on the Fatou set is "regular", while on the Julia...
left: The Heighway dragon is also the limit set of the following iteratedfunctionsystem in the complex plane: f 1 ( z ) = ( 1 + i ) z 2 {\displaystyle...
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in...
Fractal flames differ from ordinary iteratedfunctionsystems in three ways: Nonlinear functions are iterated in addition to affine transforms. Log-density...
attractor, or the fixed point, of any iteratedfunctionsystem (IFS). Starting with any point x0, successive iterations are formed as xk+1 = fr(xk), where...
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...
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...
In mathematics, the collage theorem characterises an iteratedfunctionsystem whose attractor is close, relative to the Hausdorff metric, to a given set...
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...
dynamical system Graph dynamical system Topological dynamical system List of chaotic maps Logistic map Lorenz attractor Lorenz-96 Iteratedfunctionsystem Tetration...
venue for iteration of systems of functions rather than a single function. For infinite compositions of a single function see Iteratedfunction. For compositions...
an Iteratedfunctionsystem using the set of contraction mappings { d 0 , d 1 } {\displaystyle \{d_{0},\ d_{1}\}} . But the result of an iterated function...
the iteratedfunction sequence x, f (x), f (f (x)), f (f (f (x))), ... converges to the fixed point. This concept is very useful for iteratedfunction systems...
iterated exponentials, as it is common to call expressions of this form iterated exponentiation, which is ambiguous, as this can either mean iterated...
practical functions that are defined in advance by the consciously selected arrangements of all the possible characteristics of symmetry. The spidron system is...
models. The fern code developed by Barnsley is an example of an iteratedfunctionsystem (IFS) to create a fractal. This follows from the collage theorem...
change in a single variable can have an unpredictable outcome. Iteratedfunctionsystems (IFS) – use fixed geometric replacement rules; may be stochastic...
Global Information
