Applying micro-patterns to surfaces has been shown to impart useful physical properties such as drag reduction and hydrophobicity. However, current manufacturing techniques cannot produce micro-patterned surfaces at scale due to high-cost machinery and inefficient coverage techniques such as raster-scanning. In this work, we use multiple robots, each equipped with a patterning tool, to manufacture these surfaces. To allow these robots to coordinate during the patterning task, we use the ergodic control algorithm, which specifies coverage objectives using distributions. We demonstrate that robots can divide complicated coverage objectives by communicating compressed representations of their trajectory history both in simulations and experimental trials. Further, we show that robot-produced patterning can lower the coefficient of friction of metallic surfaces. This work demonstrates that distributed multi-robot systems can coordinate to manufacture products that were previously unrealizable at scale.