Iterated Function System
In mathematics, iterated function systems or IFSs are a method of constructing fractals; the resulting constructions are always self-similar.
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 Sierpinski gasket also called the Sierpinski 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.
Read more about Iterated Function System: Definition, Properties, Constructions, Examples, History
Famous quotes containing the words iterated, function and/or system:
“The customary cry,
‘Come buy, come buy,’
With its iterated jingle
Of sugar-bated words:”
—Christina Georgina Rossetti (1830–1894)
“The fact remains that the human being in early childhood learns to consider one or the other aspect of bodily function as evil, shameful, or unsafe. There is not a culture which does not use a combination of these devils to develop, by way of counterpoint, its own style of faith, pride, certainty, and initiative.”
—Erik H. Erikson (1904–1994)
“We recognize caste in dogs because we rank ourselves by the familiar dog system, a ladderlike social arrangement wherein one individual outranks all others, the next outranks all but the first, and so on down the hierarchy. But the cat system is more like a wheel, with a high-ranking cat at the hub and the others arranged around the rim, all reluctantly acknowledging the superiority of the despot but not necessarily measuring themselves against one another.”
—Elizabeth Marshall Thomas. “Strong and Sensitive Cats,” Atlantic Monthly (July 1994)