# Micro-and nanotechnology via reaction–diffusion

## Context

The term reaction-diffusion is used to describe systems in which the components are both reacting with in some way (local production/consumption) and diffusing. The general form of the PDE for these systems is <math>\partial_t C_i =\nabla \cdot(D_i\nabla C_i)+R_i(\{C\},r,t) </math>

where <math>C_i </math>is the concentration of the ith component and <math>D_i</math> and <math>R_i</math> the diffusive and reactive constants of the ith component. The reaction-diffusion (RD) equation first gained interest after Turing showed that a system obeying this equation could display spontaneous pattern formation. Since then, many phenomena in nature have been found to obey RD. Zebra stripes, cave stalactites, and certain chemical reactions are all patterns that can be described as an outcome of RD.

As nature is able to use RD to form intricate patterns, the questions arises whether or not we can utilize this method as a way to fabricate patterns. This paper describes some techniques that were used to controllably engineer micro- and nano-patterns.