We investigate the parallel assembly of two-dimensional, geometrically-closed modular target structures out of homogeneous sets of macroscopic components of varying anisotropy. The yield predicted by a chemical reaction network (CRN)-based model is quantitatively shown to reproduce experimental results over a large set of conditions. Scaling laws for parallel assembling systems are then derived from the model. By extending the validity of the CRN-based modelling, this work prompts analysis and solutions to the incompatible substructure problem.

We present an experimental study of the kinetics of orbitally-shaken, sliding macroscopic particles confined to a two-dimensional space bounded by walls. Discounting the forcing action of the external periodic actuation, the particles undergo a qualitative transition from a ballistic to a diffusive motion regime with time. Despite the deterministic input of kinetic energy provided by the shaker, the particles show translational velocities and diffusivity consistent with a confined random walk model. Such experimental system may therefore represent a suitable macroscopic analog to investigate aspects of molecular dynamics and self-assembly.

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Dipole words are sequences of magnetic dipoles, in which alike elements repel and opposite elements attract. Magnetic dipoles contrast with more general sets of bonding types, called glues, in which pairwise bonding strength is specified by a glue function. We prove that every glue function g has a set of dipole words, called a dipole code, that attractively encodes g: the pairwise attractions (positive or non-positive bond strength) between the words are identical to those of g. Moreover, we give such word sets of asymptotically optimal length. Similar results are obtained for a commonly used subclass of glue functions.