 In mathematics , a finite subdivision rule is a recursive way of dividing a polygon or other two @-@ dimensional shape into smaller and smaller pieces . Subdivision rules in a sense are generalizations of fractals . Instead of repeating exactly the same design over and over , they have slight variations in each stage , allowing a richer structure while maintaining the elegant style of fractals . Subdivision rules have been used in architecture , biology , and computer science , as well as in the study of hyperbolic manifolds . Substitution tilings are a well @-@ studied type of subdivision rule . 
