Editing L-system (section)

===Bi-directional grammars===
The bi-directional model explicitly separates the symbolic rewriting system from the shape assignment. For example, the string rewriting process in the Example 2 (Fractal tree) is independent on how graphical operations are assigned to the symbols. In other words, an infinite number of draw methods are applicable to a given rewriting system.

The bi-directional model consists of 1) a forward process constructs the derivation tree with production rules, and 2) a backward process realizes the tree with shapes in a stepwise manner (from leaves to the root). Each inverse-derivation step involves essential geometric-topological reasoning. With this bi-directional framework, design constraints and objectives are encoded in the grammar-shape translation. In architectural design applications, the bi-directional grammar features consistent interior connectivity and a rich spatial hierarchy.<ref>Hua, H., 2017, December. [https://www.researchgate.net/profile/Hao_Hua/publication/311357805_A_Bi-Directional_Procedural_Model_for_Architectural_Design/links/5a29fb8baca2728e05dafa4b/A-Bi-Directional-Procedural-Model-for-Architectural-Design.pdf A Bi‐Directional Procedural Model for Architectural Design]. In Computer Graphics Forum (Vol. 36, No. 8, pp. 219-231).</ref>