Modeling Natural Root Branching with Geometric and Reaction Diffusion Approaches

Branching structures are ubiquitous in nature, appearing in phenomena such as thunder, fungi, and plant growth. In plants, root systems exemplify complex branching formations necessary for structural support, anchorage, and nutrient uptake. This paper presents two computational models for simulating root branching, focusing on both architectural archetypes and tropism responses. The first model employs a geometric stochastic approach to represent primary and adventitious root types in both 2D and 3D, using variable branching angles and orders to replicate distinct structural patterns. The second, more advanced model, the Reaction-Diffusion Root Branching (RDRB) model, utilizes reaction-diffusion equations within a finite element method (FEM) framework in 1D and 2D to capture the influence of biochemical, biophysical, and tropism stimuli on root development. Both models qualitatively emulate real-world root growth, with parameters calibrated through visual analysis of empirical root data. These simulations provide baseline tools for future models that incorporate environmental interactions, such as obstacles or heterogeneous nutrient distributions. Furthermore, the modeling techniques extend beyond root plants, offering a framework for exploring other natural branching systems.