The NBI software is equipped with a number of specially designed techniques for data processing, which enable it to perform automated unsupervised data clustering. Its ability to proactively search for order in chaos is well demonstrated by the following examples. Two sets of points, 129 and 244, respectively, of different configurations (see Fig. 1 and 2) were processed. The animation illustrations in Fig. 1 and 2 show the dynamics of the program's reasoning process. They also illustrate the isoclustering technique that allows delineating, in one plot, the areas of clusters of different hierarchical levels. The hierarchical character of the clustering performed by the NBI-algorithm is clearly seen in Fig. 1, where one can trace the path that brings the red point (marked "nota bene") to the group of the lowest hierarchical level; as well as in Fig. 2 showing the part of the clustering process whereupon cluster R is separated from other points in the plot.

The performance of the algorithm that employs inductive logic elements for the analysis of input information and not merely processes sets of numbers does not depend on the form of numeric expression of a problem to be solved as much as it does in mechanical methods of computing. For instance, in the above-discussed examples (Fig. 1 and 2), the clustering was performed based on similarity matrices constructed according to an exponential equation:

where Sij is a coefficient of similarity between i and j, B is a positive number, and Vi and Vj are variables of i and j . Dissimilarity matrices calculated for the same data by using Euclidean distances look totally different from the respective similarity matrices made with the use of the above equation, however, upon processing by the NBI-algorithm, they yield practically the same clustering results. In general, one and the same conclusion can be drawn based on indefinitely large number of numerically different matrices corresponding to the same set of data. In other words, the "thinking algorithm" is not a "slave of numbers" - it is capable of abstraction.