Narrow Results

Self-assembly is ubiquitous in physics, chemistry and biology, and has many applications in materials science and engineering. Here we present a general approach for finding the simplest set of building blocks that will assemble into a given physical structure. Our procedure can be adapted to any given geometry, and thus to any given type of physical system. The amount of information required to describe this simplest set of building blocks provides a quantitative measure of the structure's physical complexity, which is capable of detecting any symmetry or modularity in the underlying structure.We also introduce the notions of joint, mutual and conditional complexity for self-assembling structures. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by using it to quantify the physical complexity of protein complexes.