Toward Interactions through Information in a Multifractal Paradigm

• Main Authors: Maricel Agop, Alina Gavriluț, Claudia Grigoraș-Ichim, Ștefan Toma, Tudor-Cristian Petrescu, Ștefan Andrei Irimiciuc
• Format: Article
• Language: English
• Published: MDPI AG 2020-09-01
• Series: Entropy
• Subjects: Shannon information; multifractal theory of motion; Cayley–Klein-type absolute geometries; harmonic mapping; Lobachevsky plane; Poincaré metric
• Online Access: https://www.mdpi.com/1099-4300/22/9/987

In a multifractal paradigm of motion, Shannon’s information functionality of a minimization principle induces multifractal–type Newtonian behaviors. The analysis of these behaviors through motion geodesics shows the fact that the center of the Newtonian-type multifractal force is different from the center of the multifractal trajectory. The measure of this difference is given by the eccentricity, which depends on the initial conditions. In such a context, the eccentricities’ geometry becomes, through the Cayley–Klein metric principle, the Lobachevsky plane geometry. Then, harmonic mappings between the usual space and the Lobachevsky plane in a Poincaré metric can become operational, a situation in which the Ernst potential of general relativity acquires a classical nature. Moreover, the Newtonian-type multifractal dynamics, perceived and described in a multifractal paradigm of motion, becomes a local manifestation of the gravitational field of general relativity.