A Framework for Designing Novel Magnetic Tiles Capable of Complex Self-assemblies

Abstract

Self-assembly has been immensely successful in creating complex patterns at the molecular scale. However, the use of self-assembly techniques at the macroscopic level has so far been limited to the formation of simple patterns. For example, in a number of prior works, self-assembling units or tiles formed aggregates based on the polarity of magnetic pads on their sides. The complexity of the resulting assemblies was limited, however, due to the small variety of magnetic pads that were used: namely just positive or negative polarity. This paper addresses the key challenge of increasing the variety of magnetic pads for tiles, which would allow the tiles to self-assemble into more complex patterns. We introduce a barcode scheme which potentially allows for the generation of arbitrarily complex structures using magnetic self-assembly at the macro-scale. Development of a framework for designing such barcode schemes is the main contribution of the paper. We also present a physical model based on Newtonian mechanics and Maxwellian magnetics. Additionally, we present a preliminary software simulation system that models the binding of these tiles using magnetic interactions as well as external forces (e.g. wind) which provide energy to the system. Although we have not performed any physical experiments, nevertheless, we show that it is possible to use the simulation results to extract a higher level kinetic model that can be used to predict assembly yield on a larger scale and provide better insight into the dynamics of the real system.