Design and Simulation of Novel Magnetic Tiles Capable of Complex Self-Assemblies Urmi Majumder 1 and John H Reif 1 Department of Computer Science, Duke University urmim@cs.duke.edu, reif@cs.duke.edu Summary. As manufacturing and robotics reduces in size scale, there is an increasing need to make use of bottom-up self-assembly techniques rather than conventional top-down assembly techniques. This approach has been very successful at the molecular scale, resulting in com- plex patterning at that scale not previously achievable via conventional methods. However, the use of self-assembly techniques at a size range- between 100’s nm to 100’s of μm has so far been limited to the formation of patterns of quite limited complexity. For example, in a number of prior works self-assembling units or tiles had their sides fitted with magnets which we will call magnetic pads that allowed (or selectively disallowed) for the binding between distinct tiles to form assemblies of tiles. The complexity of the resulting assemblies was limited due to the very limited variety of magnetic pads that were currently used: namely just positive or negative polarity. This paper address the key challenge of increasing the variety of magnetic pads for tiles, which will allow the tiles to self-assemble into patterns of increased complexity governed by the selection of the pads of the tiles. In particular, we describe a family of barcode schemes that provide a much larger variety of magnetic pads. The introduction of these barcode schemes potentially allows for the generation of arbitrary complex structures using magnetic self- assembly at the meso-scale. The design and optimization of our barcode schemes for magnetic pads is the main con- cern and focus of this paper. We present a physical model based on Newtonian mechanics and Maxwellian magnetics and software simulation system that correctly models attachment, orientation and binding of macroscopic tiles using magnetic interaction as well as external forces (wind) which provide energy to the system. In particular, the simulation system allows us to determine the optimal parameters for the design and arrangement of the magnetic pads that selectively bind (or do not bind) with other tiles. We also demonstrate how we can use our simulation model to extract a thermodynamic model which can be used to predict yield of assembly on a larger scale and to provide better insight into the dynamics of our physical system. 1 Introduction Self-assembly is the autonomous organization of components into structures with- out human intervention. It is a phenomenon that is prevalent on all scales, from molecules to galaxies. Though self-assembly is a bottom-up process not utilizing an overall central control, it is theoretically capable of constructing arbitrary com- plex objects, and nature uses it to assemble what may be the most complex thing in the universe: namely humans.