 A subdivision rule takes a tiling of the plane by polygons and turns it into a new tiling by subdividing each polygon into smaller polygons . It is finite if there are only finitely many ways that every polygon can subdivide . Each way of subdividing a tile is called a tile type . Each tile type is represented by a label ( usually a letter ) . Every tile type subdivides into smaller tile types . Each edge also gets subdivided according to finitely many edge types . Finite subdivision rules can only subdivide tilings that are made up of polygons labelled by tile types . Such tilings are called subdivision complexes for the subdivision rule . Given any subdivision complex for a subdivision rule , we can subdivide it over and over again to get a sequence of tilings . 
