In order to solve the declining influence of traditional cultural symbols, the research on traditional cultural symbols has become more meaningful. This article aims to study the application of traditional cultural symbols in art design under the background of artificial intelligence. In this paper, a fractal model with self-combined nonlinear function changes is constructed. By combining nonlinear transformations and multiparameter adjustments, various types of fractal models can be automatically rendered. The convolutional neural network algorithm is used to extract the characteristics of the style picture, and it is compared with the trained picture many times to avoid the problem of excessive tendency of the image with improper weight. The improved L-BFGS algorithm is also used to optimize the loss of the traditional L-BFGS, which improves the quality of the generated pictures and reduces the noise of the chessboard. The experimental results in this paper show that the improved L-BFGS algorithm has the least loss and the shortest time in the time used for more than 500s. Compared with the traditional AdaGrad method, its loss is reduced by about 62%; compared with the traditional AdaDelta method, its loss is reduced by 46%. Its loss is reduced by about 8% compared with the newly optimized Adam method, which is a great improvement.
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