Reconstruction and Practical Application of Higher Vocational Mathematics Teaching Guided by Fractal Theory

分形理论作为一种描述自然界复杂结构和不规则现象的关键工具，近些年来在多个领域取得了显著的应用成果。基于自相似性与分形维数等核心概念，该理论揭示了从微观到宏观尺度广泛存在的非线性规律。本文系统地阐述了分形理论的数学基础，并针对其在专科院校教学实践中面临的挑战提出了具体的解决方案。研究旨在为分形理论的理论深化及其工程化应用提供全面的参考依据，同时为职业教育培养具备复杂系统思维的技术人才探索创新路径。Fractal theory, as a critical tool for characterizing complex structures and irregular phenomena in nature, has demonstrated substantial application value across multiple domains in recent years. Built upon foundational concepts such as self-similarity and fractal dimension, this theory reveals nonlinear laws that are prevalent at both microscopic and macroscopic scales. This paper systematically elucidates the mathematical foundations of fractal theory and addresses specific challenges encountered during its implementation in vocational college teaching practices by proposing targeted solutions. The study aims to provide a comprehensive reference framework for advancing the theoretical exploration and engineering applications of fractal theory, while also exploring innovative strategies for vocational education to cultivate technical talents with complex system thinking capabilities.