Geometry of Plane Transformations

Affine transformations of the plane are compositions of scalings, reflections, rotations, and translations.

Here is the matrix formulation of an affine transformation.

The order of these transformations is important. For example, reflecting then translating can give a different result from translating then reflecting.

We adopt this convention: scalings first, reflections second, rotations third, and translations last. (This is implied by the matrix formulation.) Emphasizing this order, the components of a transformation are encoded in tables of this form

With this encoding of transformations of the plane, we can now make fractals using the method called Iterated Function Systems (IFS).

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