  The Arbitrary Pattern Formation problem asks to design a distributed
algorithm that allows a set of autonomous mobile robots to form any specific
but arbitrary geometric pattern given as input. The problem has been
extensively studied in literature in continuous domains. This paper
investigates a discrete version of the problem where the robots are operating
on a two dimensional infinite grid. The robots are assumed to be autonomous,
identical, anonymous and oblivious. They operate in Look-Compute-Move cycles
under a fully asynchronous scheduler. The robots do not agree on any common
global coordinate system or chirality. We have shown that a set of robots can
form any arbitrary pattern, if their starting configuration is asymmetric.
