Julia Set Fractal: c = 0.38 + 0.34i in the Complex Plane

This GeoGebra example visualizes the Julia set fractal for a fixed complex parameter c = 0.38 + 0.34i. It iterates the function z → z² + c on the complex plane, coloring points based on whether the iteration diverges to infinity or remains bounded, producing intricate self-similar boundary patterns. Core mathematical concepts include complex arithmetic, iteration, dynamical systems, fractal geometry, and convergence/divergence criteria. The construction uses the First command to extract initial elements from lists, creates numerous point objects (A1 to A21) and a list (lijst2) to store iteration trajectories, employs a slider (knop1) to control iteration depth or parameters, uses a grid (raster) for coordinate reference, and incorporates image objects (afbeelding1, afbeelding2) for enhanced visuals. This resource is suitable for high school to university students studying complex numbers, fractals, or computational visualization, and serves as an engaging tool for exploring chaotic behavior in complex iteration.