Research on structural surface feature refinement method based on fractal geometry in industrial design

Fractal geometry is an emerging discipline that has developed rapidly in recent decades, and its study of irregular geometric shapes can be used to describe objects in nature that cannot be described by traditional geometry, and it has a broad space for development and application prospects.In this paper, the theory of fractal geometry is applied to industrial design to realize the refinement and analysis of surface features.The study includes an in-depth analysis of the theory of fractal geometry, the Koch curve as an example to illustrate the principle of fractal geometry.The study also investigates different dimension calculation methods, such as Hausdorff dimension, box dimension, correlation dimension, information dimension, generalized dimension, and self-similarity dimension of fractal geometry, and proposes a dimension calculation method for the refinement of structural surface features for industrial design.After the fractal geometry surface feature refinement simulation analysis, the porosity of the fractal map based on this paper's method ranges from 16% to 38%, and the comparison with the Serpinski method proves that the presently selected fractal model is more effective in the refinement of structural surface features for industrial design.As shown by the surface feature simulation results, there is indeed a certain degree of similarity between the roughness topography of the real structural surface of the two surface processing methods in industrial design and the roughness topography simulated by the fractal function.The above study proves that the method of refining the structural surface features of industrial design based on fractal geometry in this paper is scientific and feasible.