Simulation of Programmable Matter with Mathematical Graphs

The prospect of programming matter provides an unprecedented array of potential uses in architecture, mechanical engineering, and other scientific disciplines dedicated to the creation of future technologies. Therefore, multiple firms and institutions have spearheaded efforts to develop dynamic materials and compounds easily mutable in structure with a simple, selected stimulus. This work attempts to predict the possibility of actuating programmable materials on an atomic scale, simulating the mechanics of a sixty-four-node, cubic lattice structure. Coded using the Python-based NetworkX library, each node and edge represent the particles of a selected element and the forces between each atom, respectively; the program encodes mass attributes to each node and a spring constant to each edge, values of which – by use of Hooke’s law – determine the behavior of the system upon the introduction of a simulated phonon or elastic collision. Eventually, through experimentation with discrete masses, forces, and elastic vibrations, this program demonstrates possible input combinations that change the lattice structure to a predetermined shape, leading to the possibility of replicating the simulated relationships and, hence, providing an innovative manner of manipulating matter, atom by atom.