In this paper we introduce and apply a novel approach for self-organiz- ation, partitioning and pattern formation on the non-oriented grid environment. The method is based on the generation of nodal patterns in the environment via sequences of discrete waves. The power of the primitives is illustrated by giving solutions to two geometric problems using the broadcast automata model arranged in an integer grid (a square lattice) formation. In particular we show linear time algorithms for: the problem of finding the centre of a digital disk starting from any point on the border of the disc and the problem of electing a set of automata that form the inscribed square of such a digital disk.
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