Discrete Discs and Broadcasting Sequences

Neighbourhood Sequences are deemed to be important in many practical applications within digital imaging through their application in measuring digital distance. Aggregation of neighbourhood sequences based on classical digital distance functions was proposed as an alternative method for organising swarms or robots on the non-oriented grid environment in [1]. Wave phenomena generated nodal patterns in a discrete environment via the two neighbourhood sequences providing a distributed algorithm to find the centre of a digital disc. The geometric shapes that can be formed by such sequences in 2-D are quite limited and so constraints are relaxed to allow any two points at euclidean distance r (r-neighbours) such neighbourhoods represented by the digital disc of radius r.