African Fractal Geometry as a Novel Approach to Understanding Supersymmetry: A Comparative Analysis with Calabi-Yau Manifolds

Abstract

Precious Mamotingoe Lesupi

We investigate the potential parallels between African fractal geometry, particularly in Adobe architecture, and the mathematical structures underlying supersymmetry and Calabi-Yau manifolds. Our explorations extend to how the recursive scaling properties of African fractals, described by the power law scaling dimension D= log N/ log r, might offer new insights into extra dimensions proposed by supersymmetry. We then compare the self-similarity of African fractals with the complex geometry of Calabi-Yau manifolds, characterized by the Ricci-flat condition R ij = 0. Thus, developing a novel mathematical framework that maps African fractal patternsonto higher-dimensional spaces, utilizing the supersymmetry algebra �??_�?�, �??_�?� = 2(γ_μ) _αβ Ρ_μ. This approach aims to provide a unique perspective on the geometric foundations of supersymmetry and potentially uncover new mathematical tools for visualizing and understanding higher dimensional spaces.

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