The Modular Fractal Infinity (MFI): A Novel Framework for Modeling Infinity with a Modular Fractal Dimension

This paper introduces the Modular Fractal Infinity (MFI), a novel mathematical framework that combines fractal geometry and modu- lar arithmetic to model infinite processes within a finite context. We propose a modular fractal dimension (Dm), which modifies the classi- cal fractal dimension to incorporate periodic constraints imposed by modular arithmetic. Theoretical derivations are presented, validated with examples (Sierpinski triangle and Koch snowflake), and directions for experimental verification are suggested. Potential applications in mathematics, physics, and computer science are discussed.