Fatou set

In mathematics, a Fatou set is defined informally as the largest open set of points on which iterations of a given map (or collection of maps) have relatively tame long-term behaviour, in the sense that points that start close together stay close together. A map's Fatou set is the complement of its Julia set.

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Less commonly, the term Fatou set or Fatou dust is sometimes used to refer to a Julia set that is not connected.

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Fatou sets are named after French mathematician Pierre Fatou.

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Iteration: :This article discusses a concept which is exploited in computer programming (but which originated before it). For use in the Japanese and Chinese languages see iteration mark....

Map: A map is a simplified depiction of a space, a navigational aid which highlights relations between objects within that space. Most usually a map is a two-dimensional, geometrically accurate representation of a three-dimensional space. The science and art of map-making is cartography....

Julia set: Julia sets, described by Gaston Julia, are fractal shapes defined on the complex number plane. Given an iterated map of the complex plane to itself, or a collection of such maps, the Julia set for this system can be defined (informally) as the set of points for which nearby points do not exhibit si...

Fatou set related Images and Photos (experimental)

Smart Set (DVD)	Ready, Set, Green Book (Paperback)	House Set	Kekkaishi Set 1 (DVD)
Matching Set I	Smart Set (On Demand)	SET IT OFF (2PK/DVD/BD)	Kekkaishi Set 2
Set It Off DVD	Kekkaishi Set 3	Kekkaishi Set 4	Set of Crayons