iterated polynomial - translation to ρωσικά
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iterated polynomial - translation to ρωσικά

METHOD ALLOWING THE CONSTRUCTION OF SELF-SIMILAR FRACTALS
Iterated function systems; Iterated Function System; Iterated Function Systems
  • Construction of an IFS by the [[chaos game]] (animated)
  • Apophysis]] software and rendered by the [[Electric Sheep]].
  • IFS "tree" constructed with non-linear function Julia
  • [[Barnsley's fern]], an early IFS
  • IFS being made with two functions.
  • [[Menger sponge]], a 3-Dimensional IFS.
  • [[Sierpinski triangle]] created using IFS (colored to illustrate self-similar structure)

iterated polynomial      

математика

итерированный многочлен

ring of polynomials         
ALGEBRAIC STRUCTURE
Polynomial algebra; Integral polynomial; Ring of polynomials; Free commutative algebra; Free commutative ring; Integer Polynomial; Polynomial expression; Multivariate polynomial ring; Polynomial rings

математика

кольцо многочленов

polynomial expression         
ALGEBRAIC STRUCTURE
Polynomial algebra; Integral polynomial; Ring of polynomials; Free commutative algebra; Free commutative ring; Integer Polynomial; Polynomial expression; Multivariate polynomial ring; Polynomial rings

математика

многочленное выражение

Ορισμός

Iterated Function System
<graphics> (IFS) A class of fractals that yield natural-looking forms like ferns or snowflakes. Iterated Function Systems use a very easy transformation that is done recursively. (1998-04-04)

Βικιπαίδεια

Iterated function system

In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. 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 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.

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