Several Fractal Patterns of Julia Sets with MATLAB Implementation

This article presents several fractal patterns of Julia sets along with original MATLAB source code. Julia sets represent a class of complex function sets that exhibit fascinating geometric properties. These fractal diagrams demonstrate fundamental characteristics of Julia sets, including self-similarity and intricate complexity. The provided MATLAB implementation allows for deeper exploration of the generation process and design principles behind these fractal patterns. The code includes detailed comments explaining each computational step and its significance, covering critical aspects such as complex number iteration algorithms, escape-time calculations, and color mapping techniques. Key MATLAB functions utilized in the implementation include meshgrid for coordinate system setup, array operations for efficient complex number calculations, and customized colormap functions for visualization enhancement. Through studying these fractal patterns and their computational implementation, readers can advance their mathematical and computer science skills while gaining profound aesthetic appreciation of mathematical beauty.