Editing Iterated function system (section)

{{Short description|Method for the construction of fractals}}
[[File:Sierpinski1.png|thumb|right|250px|[[Sierpinski triangle]] created using IFS (colored to illustrate self-similar structure)]]
[[File:Chris Ursitti fractal 0000.png|thumb|right|200px|Colored IFS designed using [[Apophysis (software)|Apophysis]] software and rendered by the [[Electric Sheep]].]]
In [[mathematics]], '''iterated function systems''' ('''IFSs''') are a method of constructing [[fractal]]s; the resulting fractals are often [[self-similar]]. IFS fractals are more related to [[set theory]] than fractal geometry.<ref name="picg">{{cite book |title=Progress in Computer Graphics: Volume 1 |last=Zobrist |first= George Winston |author2=Chaman Sabharwal |year=1992 |publisher=Intellect Books |isbn=9780893916510 |page=135 |url=https://play.google.com/store/books/details?id=Ai6Qo0qoE9EC |access-date=7 May 2017}}</ref> 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 [[contraction mapping|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.