Arjun Chandrasekhar
department of Math and Computer Science at Southwestern University in Georgetown, Texas, USA

The roots of wild tomato plants can be modeled as a Euclidean graph made up of the line segments comprising the main root and lateral roots. These biological networks attempt to minimize the total amount of material used (wiring cost) and minimize the time needed to transport resources to the base of the main root (conduction delay). These conditions compete against each other, therefore minimizing both simultaneously is generally impossible. In order to account for this trade off, we attempt to optimize the network under the theory of Pareto optimality. This talk explores the attempts of both analytical and algorithmic methods of generating a model for the growth of these roots under the effects of gravity. The addition of the gravity variable expands a previous model explored. We will discuss the creation and application of an algorithm to compute the Pareto front of root structures that achieve an optimal balance between wiring cost and conduction delay within a given set of gravitropic conditions. We will explore how the algorithmically modeled roots compare to actual scans of tomato roots. This talk will also discuss the progress made to find an analytical solution to this model, and the challenges that face an analytically-produced model.