Chapter 5: Two Dimensions and Beyond

Section 4: Substitution Systems and Fractals

Affine transformations

Any set of so-called affine transformations that take the vector for each point, multiply it by a fixed matrix and then add a fixed vector, will yield nested patterns similar to those shown in the main text. Linear operations on complex numbers of the kind discussed above correspond geometrically to rotations, translations and rescalings. General affine transformations also allow reflection and skewing. In addition, affine transformations can readily be generalized to any number of dimensions, while complex numbers represent only two dimensions.

From Stephen Wolfram: A New Kind of Science [citation]