1. A new method of quantifying spatial pattern was introduced for two-dimensional mapped data, with an associated index of aggregation and a test for departures from randomness, based on an attractive algorithm in which individuals in the sample move to a regular arrangement which resembles a hexagonal lattice, using Voronoi tessellations. The algorithm incorporates a biological model for the dispersal of individuals from a source, in which each individual is assigned a dynamic territory. The method is one of a class known as Spatial Analysis by Distance IndicEs (SADIE). 2. Two diagnostic plots were introduced, each based on the distance of the sample from the final, regular arrangement, to aid the description of the observed spatial pattern. 3. By backtracking from the observed sample points away from the final arrangement, the presence of clusters in the sample may be detected more easily, and heuristic estimates derived of the cluster foci. 4. Examples are given for seven sets of data, with analyses of over 20 subsets at several spatial scales, concerning: aphids, beetle larvae, ant mounds, sparrowhawk nesting territories, pine seedlings, redwood seedlings, and biological cells.