Studying Turing patterns in vegetation

Reaction-diffusion equations are a widely studied class of mathematical models that describe systems in which the rate of change of each state variable is determined by local interactions between the variables and their diffusion in space. In 1952, Alan Turing discovered a mechanism by which small random perturbations from an initially homogeneous equilibrium state could cause the development of complex spatial patterns in certain reaction-diffusion systems. This provides an explanation for patterns observed in many areas of ecology, physics, and developmental biology. In this work we show experimental measurements of Turing patterns in vegetation obtained in space using chia seeds growing in four different substrates with varying levels of diffusion, daily irrigation, and evaporation. We developed interactive GPU simulations of a 2D reaction-diffusion model of vegetation growth (Rietkerk) with model parameters fitted to the experiments. We demonstrate that the model is able to reproduce the experimental patterns for the different levels of diffusion, irrigation, and evaporation. We believe this is the first time a vegetation model has been validated directly with experiments.