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Iterated functions systems are a kind of fractal that was
conceived in its present form by John Hutchinson in 1981 and
popularized by Michael
Barnsley's book Fractals Everywhere.
IFS fractals as they are normally called can be of any number of dimensions, but are commonly computed and
drawn in 2D. An IFS fractal is a solution to a recursive set equation. 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 Sierpinski gasket. The functions are normally "contractive" which means
they bring points closer together and makes 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.
Formally, where and
The most common algorithm to compute IFS fractals is called the chaos game. It consists of picking a random point in the plane, then iteratively applying one
of the functions chosen at random from the function system and drawing the point.
Fractal flames are a generalization and refinement of IFS
fractals.
Barnsley tried to use IFS to encode images and received a patent for his efforts. But his claims were exaggerated and the
company failed.
Random game IFS from a set using five linear and then two
nonlinear transformations in sequence.
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