Reaction kinetics coupled to diffusion can result in synergism leading to the formation of stable and temporal patterns. Reaction-diffusion system have served as the prototype for the study of complexity. One prominent example is the concept of Turing patterns, which describes how particular patterns observed in nature, such as stripes and spots, can naturally arise out of a homogeneous, uniform system.
Within this project, you will design a computational routine that simulates a two-compound / two-dimensional reaction diffusion system. You will explore which type of kinetics coupled to a diffusion system gives rise to stable or temporal patterns. Building upon these results, you can either explore pattern formation in higher dimensions (i.e. three-dimensional space) or explore which patterns can be found when dealing with more than two compounds in the system.
Figure 1: Reaction-diffusion system leading to stripe formation.
Figure 2: Reaction-diffusion system leading to spot formation.