Abstract-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.

No abstract