Julia Set: c = -0.11 + 0.6557i Fractal in the Complex Plane
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This example demonstrates the Julia set fractal in the complex plane for the fixed parameter c = -0.11 + 0.6557i. It iterates the map z → z² + c for each point z and colors points based on whether the iteration diverges or remains bounded. Core mathematical concepts include complex numbers, iteration, dynamical systems, fractal geometry, and convergence/divergence in the complex plane. Construction highlights: uses the GeoGebra command First, along with numerous point objects (A, A1, A2, ... A21) and a list lijst2 to store iterated points, a slider or button (knop1) to control iteration depth, and a raster grid (raster) with images (afbeelding1, afbeelding2) for visualization. Suitable for high school to university students studying complex numbers, fractals, and iteration, as well as for mathematical exploration and artistic creation.
GeoGebra Commands & Parameters
First(A1:A21, s + 1) → lijst2
AI Drawing Prompt Reference
Create a Julia set in the complex plane with parameter c = -0.11 + 0.6557i. Use the iteration formula z → z² + c for each point z, and color the points based on whether the iteration diverges. Adjust the iteration depth with a slider and generate the image.
The prompt above was compiled from the original drawing commands and is for reference only.