Abstract

The objective of this article is to offer an interpretation of the utopian society described in Plato's Republic from a simplified theory of fractals. Plato conceptualizes his Republic as a static society in terms of structure and its components, the people, as having a behavior that can be programmed as linear and not dynamic (LNDS). Based on this analogy, real social functioning (NLDS) is conceptualized, applying the concept of fractal and its corresponding fracton, as the force of attraction that acts in social groups. Thus, social groups obey a fractal geometry, a geometry that reproduces the pyramidal shape, the apex being the crystallization of authority, power or leadership. Modern society, in analogy with Plato's Republic, is also a fractal production machine, replicating pyramid-shaped hierarchical structures and the respective fractons. Individuals are the basic unit of all these fractals. They are the building blocks of all groups at all levels of society. But replication is not self-similar due to fluctuations in cognition and behavior.