Making self-disassembling objects with multiple components in the Robot Pebbles system

This paper describes several novel algorithms for shape formation by subtraction in programmable matter systems. These algorithms allow the simultaneous formation of multiple different shapes from a single block of host material. The resulting shapes are allowed to intertwine in arbitrarily complex ways. We also present a proof that the algorithms operate correctly to form the desired shapes. Finally, we show experimental results from close to 100 trials using both the Robot Pebbles hardware and a unique software simulator. Multiple trials of several different experiments demonstrate the algorithms operating correctly.