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 function of muscle is to pull and not to push, except in the case of the genitals and the tongue.”
—Leonardo Da Vinci (1425–1519)
“All who wish to hand down to their children that happy republican system bequeathed to them by their revolutionary fathers, must now take their stand against this consolidating, corrupting money power, and put it down, or their children will become hewers of wood and drawers of water to this aristocratic ragocracy.”
—Andrew Jackson (1767–1845)