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*[[Cantor function]] *[[Iterated function system]] ...

...tosh Platform and the redesigned Windows Version 2.0 product. The Genuine Fractals products were acquired by [[LizardTech]] in June 2001, before ultimately be ...s|PIFS (partitioned iterated function systems)]]. When scaling up, Genuine Fractals exploits the [[self-similarity]] of an image to increase its size while pre ...

{{Short description|Method for the construction of fractals}} ...cting [[fractal]]s; the resulting fractals are often [[self-similar]]. IFS fractals are more related to [[set theory]] than fractal geometry.<ref name="picg">{ ...

'''Fractal flames''' are a member of the [[iterated function system]] class<ref>Mitchell Whitelaw (2004). ''Metacreation: Art and Artificial L Fractal flames differ from ordinary iterated function systems in three ways: ...

...set of functions is called an [[Iterated function system|iterated function system (IFS)]]. Apophysis then generates the attractor of this set of functions, b ...mes, or do bigger tasks. One such instance is rendering an entire batch of fractals. ...

...s 1, and the corresponding eigenvector is the [[invariant measure]] of the system. The iterated function to be studied is a map <math>f\colon X\rightarrow X</math> for an arbitrary ...

* [[Iterated function system]], a method of constructing fractals in mathematics and computer science * [[Installable File System]], a filesystem API in IBM OS/2 and Microsoft Windows NT ...

*[[List of fractals by Hausdorff dimension]] {{Fractals}} ...

...n be approximated by [[recursion|recursive]] methods such as [[Lindenmayer system]]s. The dragon curve is probably most commonly thought of as the shape that ...Heighway dragon is also the limit set of the following [[iterated function system]] in the complex plane: ...

...iterated function]]s. Chaotic maps often occur in the study of [[dynamical system]]s. ...[[Iterated function|iterated functions]] often generate [[fractals]]. Some fractals are studied as objects themselves, as [[set (mathematics)|sets]] rather tha ...

...tion]], Cesàro–Faber curve ([[Lévy C curve]]), [[Minkowski's question mark function]], [[blancmange curve]], and the [[Koch snowflake|Koch curve]] are all exam where <math>\circ</math> denotes [[function composition]]. It can be shown that each <math>c_x</math> will map the comm ...

==L-system construction== [[Image:Levy C Curve.svg|thumb|260px|Lévy C curve (from a L-system, after the first 12 stages)]] ...

...aupe, Dietmar; Maletsky, Evan; Perciante, Terry; and Yunker, Lee (1991). ''Fractals for the Classroom: Strategic Activities Volume One'', p.21. Springer-Verlag ...may be [[iterated function|iterated]], resulting in an [[iterated function system]]. The composition of functions creates the algebraic structure of a [[mono ...

==Iterated function systems== {{Main|Iterated function system}} ...

...tle=Chaos Game}}</ref><ref>{{cite book |doi=10.1016/C2013-0-10335-2 |title=Fractals Everywhere |date=1993 |isbn=978-0-12-079061-6 |first1=Michael F. |last1=Bar ...the [[Fixed point (mathematics)|fixed point]], of any [[iterated function system]] (IFS). Starting with any point x₀, successive iterations are f ...

...that is, the value after the ''k''-th [[Iterated function|iteration of the function]] <math>f _c.</math> Thus We can introduce a new function: ...

...analysis]], a '''space-filling curve''' is a [[curve]] whose [[Range of a function|range]] reaches every point in a higher dimensional region, typically the [ [https://books.google.com/books?id=lPdQAAAAMAAJ "Fractals in the Fundamental and Applied Sciences"]. ...

...matserv.pmmf.hu/hajtas/docs/2/Spidron_EN.pdf |title=Concept of the Spidron System |last=Erdély |first=Daniel |date=2004 |access-date=2011-12-28 |url-status=d ...s also appeared, in several versions, as a public area work. Since spidron-system is the personal work by Dániel Erdély but in the development of the individ ...

...{{Citation |editor1-last=Edgar |editor1-first=Gerald A. |title=Classics on fractals |publisher=Westview Press. Advanced Book Program, Boulder, CO |series=Studi ...ractal geometry and dynamical systems in pure and applied mathematics. II. Fractals in applied mathematics. ...

{{Short description|Result of repeatedly applying a mathematical function}} ...a [[shear mapping]] with infinite order.<br><small>Below that are their [[Function composition|compositions]], which both have order 3.</small>]] ...