Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Finite subdivision rule
open-in-new
<p>In mathematics, a finite subdivision rule is a recursive way of dividing a <a href="/facts/Polygon/xvkmYhvG">polygon</a> or other two-dimensional shape into smaller and smaller pieces. Subdivision rules in a sense are generalizations of regular geometric <a href="/facts/Fractals/sXj38JeN">fractals</a>. 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 <a href="/facts/Hyperbolic_manifold/eUBhz9uW">hyperbolic manifolds</a>. <a href="/facts/Substitution_tiling/q66458WM">Substitution tilings</a> are a well-studied type of subdivision rule. </p>