The Uniqueness and Significance of Simple Structure Demonstrated by Contrasting Organic “Natural Structure” and “Random Structure” Data

The study compares the extent to which naturally structured data and artificial, relatively random data (both with the same basic parameters) produce simple structure factors which are uniquely determined. Two examples of unstructured matrices were compared with the ball problem matrix. The results show that an oblique position of maximum hyperplane count in the structured data differs from that in the unstructured by reaching a significantly more unique position in terms of the exactitude with which it is re-discoverable when starting from different positions, and by reaching (at the maximum) a significantly higher hyperplane count.