Constructal pattern formation in stony corals, bacterial colonies and plant roots under different hydrodynamics conditions.

This paper explores a new application of the constructal theory, namely in describing and predicting the formation of dissimilar patterns inside elements of the same species under different hydrodynamics conditions. Our study proposes an explanation for the differences found in morphology of stony corals, bacterial colonies and plant roots. It specially provides an answer to the following question: have their shapes (architecture) been developed by chance, or do they represent the optimum structure serving their ultimate purpose? We show that in order to persist in time, these systems must evolve in such a way that an easy access to nutrients is ensured: their shapes develop in such a way as to minimize the time to reach the nutrient source. Moreover, it is also shown that it is the combination of a dispersive (diffusive) and a convective mechanism that allows for the maximization of nutrient transfer through use of the best of these mechanisms at a specific time. In the light of this outcome, it is straightforward to conclude why the existence of an optimal architecture makes sense: it is because there is an overriding natural tendency and because the system has the freedom to morph its shape in the search for an optimal attainment of this goal within a set of constraints imposed by the situation.