This paper realizes the productized application of fractal geometric aesthetics through parametric modeling and fractal algorithm. Firstly, we systematically analyze the mathematical principles of fractal generation such as Hilbert curve, Piano curve, etc., and construct the mapping relationship between fractal forms and product decoration patterns. A Grasshopper-based fractal parametric design framework is proposed to realize the dynamic evolution and functional adaptation from two-dimensional fractal patterns to three-dimensional product forms. The fractal algorithm is developed, combining recursive algorithm and iterative algorithm optimization with grayscale symbiotic matrix feature screening mechanism to quantitatively evaluate the adaptability of fractal texture in the visual representation of products. The fractal algorithm in this paper generates images with higher accuracy, with an average accuracy of 86.77%, while the average satisfaction is improved by 12.35% over the traditional algorithm.
