Fractal Art Graphic Design Based on Newton's Iterative Algorithm

This study addresses critical limitations of traditional Newton iteration methods in fractal generation—namely sensitivity to initial values, narrow convergence domains, and instability with complex functions—by introducing an enhanced algorithm with two key innovations: (a) an adaptive initial value selection mechanism that dynamically optimizes starting points based on function characteristics and (b) a real-time dynamic step-size adjustment strategy that uses derivative feedback to correct iteration parameters. Validated in MATLAB, the proposed algorithm achieves a 45% reduction in average iterations (from 11 to 6), increases convergence success from 80.5% to 95.8%, and reduces computation time by half (4.2s to 2.1s). The generated fractals exhibit significantly improved detail scores (80 to 94) and enhanced artistic expressiveness, demonstrating efficient high-resolution fractal synthesis with improved convergence stability for computational art applications.