Based on work of Mandelbrot and Hutchinson, and popularized by Barnsley, iterated function systems (IFS) is a method for generating fractals by using affine transformations (linear transformations plus translations). This is a powerful way to reveal the simplicity underlying some complex shapes, and serves as an excellent catalyst for discussing just what constitutes visual complexity. For example, the shape on the left is generated with an IFS using three transformations, the shape on the right by an IFS using six.
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We begin with the most straightforward approach, Deterministic IFS.
A prelude to the random algorithm for generating IFS is the Chaos Game.
A variation on Random IFS is the method we use to analyze data.
Finding the IFS to produce a given shape is the the Inverse Problem.
The relations between the parts of an IFS image can be effectively revealed through some animations.
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