Substitution tilings. The term substitution, in connection with tilings, describes a simple but powerful method to produce tilings with many interesting properties.

The main idea is to use a finite set of building blocks called prototiles, an expanding linear map (the inflation factor), and a rule how to dissect each scaled tile into copies of the original prototiles.

For some examples of substitution tilings, and a glossary of terminology, see the tilings encyclopedia at http://tilings.math.uni-bielefeld.de/