Abstract
This paper provides a framework for understanding and analyzing non-differentiable fractal manifolds. By introducing specialized mathematical concepts and equations, such as the Metric Tensor, Curvature Tensors, Analogue Arc Length, and Inner Product, it enables the study of complex patterns that exhibit self-similarity across different scales and dimensions. The Analogue Geodesic and Einstein Field Equations, among others, offer practical applications in physics, highlighting the relevance and potential of fractal geometry.
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