Geometry always has two parts to it: one part is the description of the objects that can be generated; the other investigates how these objects can be changed (or transformed). Any object formed by several vectors may be mapped to an arbitrarily bizarre curved or distorted object — here, we are interested in those maps that map vectors to vectors and are “benign” in some well-defined sense. All these maps may be described using the tools of matrix operations. An interesting pattern is generated from a simple square in Figure 4.1 by such “benign” 2D linear maps. Linear maps in 20: an interesting geometric figure constructed by applying 20 linear maps to a square.