From a set of parts to an indivisible whole. Part III: Holistic space of multi-object relations

TL;DR

This paper introduces a method to visualize the complex holistic space of multi-object relations using hierarchical grouping and isotropic fields, revealing intricate structures like attractor membranes and their properties.

Contribution

It presents a novel approach to simulate and analyze cooperative interactions and the holistic space of object relations through hierarchical grouping and isotropic field visualization.

Findings

Identification of complex spatial structures called attractor membranes.

Analysis of how intergroup similarities change with the drifter’s position.

Visualization of the holistic space of multi-object relations depending on object arrangement.

Abstract

The previously described methodology for hierarchical grouping of objects through iterative averaging has been used for simulation of cooperative interactions between objects of a system with the purpose of investigation of the conformational organization of the system. Interactions between objects were analyzed within the space of an isotropic field of one of the objects (drifter). Such an isotropic field of an individual object can be viewed as a prototype of computer ego. It allows visualization of a holistic space of multi-object relations (HSMOR) which has a complex structure depending on the number of objects, their mutual arrangement in space, and the type of metric used for assessment of (dis)similarities between the objects. In the course of computer simulation of cooperative interactions between the objects, only those points of the space were registered which corresponded to transitions in hierarchical grouping. Such points appeared to aggregate into complex spatial structures determining a unique internal organization of a respective HSMOR. We describe some of the peculiarities of such structures, referred to by us as attractor membranes, and discuss their properties. We also demonstrate the peculiarities of the changing of intergroup similarities which occurs when a drifter infinitely moves away from the fixed objects.