Randomness in topological models

Abstract

There are two aspects of randomness in topological models. In the first one, topological idealization of random patterns found in the Nature can be regarded as planar representations of three-dimensional lattices and thus reconstructed in the space. Another aspect of randomness is related to graphs in which some properties are determined in a random way. For example, combinatorial properties of graphs: number of vertices, number of edges, and connections between them can be regarded as events in the defined probability space. Random-graph theory deals with a question: at what connection probability a particular property reveals. Combination of probabilistic description of planar graphs and their spatial reconstruction creates new opportunities in structural form-finding, especially in the inceptive, the most creative, stage.