The optimal shape of roots

Roots provide plants with mechanical stability and pure water. Wind and gravitational forces on plants are spread out by the roots over a large volume of soil. In a similar manner, roots absorb pure water and nutrients from moist soil. These processes are mathematically similar and have similar optimal solutions, unless the soil is inhomogeneous -i.e. if one part is wetter, whereas another part provides more of a grip for the roots to hold onto. A root system with a given weight has an optimized shape if it quickly produces large amounts of clean water at a low energy cost. By understanding the optimized shape of roots we may be able to exploit this natural structure to improve water desalination systems.