Barcoded Magnetic Tiles for Programmable Assemblies∗

As manufacturing scales down, there is an increasing need to use bottomup self-assembly techniques over conventional top-down assembly techniques. Previously self-assembling units or tiles forming aggregates based on the polarity of magnetic pads on their sides have been demonstrated. These assemblies were simple, primarily because of the small variety of magnetic pads used. This paper addresses the key challenge of increasing the variety of magnetic pads for tiles, which would allow macroscopic tiles to self-assemble into more complex patterns. The main contribution of our paper is a novel barcode scheme for magnetic tile pads, and the design and optimization of our barcode scheme for magnetic pads is the paper’s major concern and focus. We present a physical model and a software simulation system that models the binding of these tiles using magnetic interactions as well as external forces. The physical model is based on Newtonian mechanics and Maxwellian magnetics. The simulation system models attachment, orientation and binding of macroscopic tiles using magnetic interaction as well as external forces (wind) which provide energy to the system. It allows us to estimate the suitable parameters for the barcode scheme for magnetic pads that selectively bind (or do not bind) with other tiles, and so to calculate the predicted interactions for two large floating ∗This paper is a revised version of the conference proceedings paper: Urmi Majumder and John H. Reif, A Framework for Designing Novel Magnetic Tiles Capable of Complex Self-Assemblies, Conference on Unconventional Computation, Vienna, Austria, Aug 25-26, 2008, Unconventional Computing, Lecture Notes in Computer Science number 105633, Springer, Berlin Heidelberg. †Oracle Corporation, Washington D.C, USA ‡Department of Computer Science, Duke University, Durham, NC , USA and Adjunct, Faculty of Computing and Information Technology (FCIT), King Abdulaziz University (KAU), Jeddah, Saudi Arabia tiles with embedded magnets. We observed that tiles that are elongated and magnetically shielded allow less cross-talk between interactions and the implementation of a magnetic bar-code for a larger number of specific bindings. We also demonstrate how we can use our simulation model to extract a scalable thermodynamic model which can be used to predict yield of assembly on a larger scale and also to provide better insight into the dynamics of our physical system.