Influence of Fractal Embedding in Three-Dimensional Euclidean Space on Wave Propagation in Electro- Chromodynamics

TL;DR

This paper investigates how different embeddings of fractal sets in three-dimensional space affect electromagnetic wave diffraction, revealing that embedding properties influence wave behavior and have implications for fractal electrodynamics and strong interaction physics.

Contribution

It introduces the impact of fractal embedding in Euclidean space on wave diffraction, highlighting a new property relevant for applications in physics.

Findings

Embedding affects wave diffraction characteristics

Fractal embedding influences electromagnetic wave behavior

Implications for fractal electrodynamics and strong interactions

Abstract

In this paper two zero-dimensional compact sets with equal topological and fractal dimensions but embedded in Euclidean space by different ways are under study. Diffraction of plane electromagnetic wave propagated and reflected by fractal surfaces is considered for each of these compact sets placed in vacuum. It is obtained, that the embedding of compact influences on characteristics of wave in final state. Thus, the embedding of Cantor set in Euclidean space is additional property of a fractal which can be important both for applications of fractal electrodynamics and for physics of strong interactions.