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Mandelbrot Set

Math Experiment Details

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📖 About This Experiment

The Mandelbrot set is a famous fractal defined by the iterative formula z = z² + c. Points that remain bounded under iteration belong to the set. This experiment visualizes the set in 3D, where height represents how quickly points escape to infinity.

💡 Key Concepts

  • Complex Numbers: Numbers with real and imaginary parts
  • Iteration: Repeatedly applying a function
  • Self-Similarity: Patterns repeat at different scales
  • Fractal Dimension: Non-integer measure of complexity
  • Escape Time: How fast values diverge to infinity

🔢 Key Formulas

Mandelbrot Iteration
z(n+1) = z(n)² + c
Complex Number
c = a + bi
Escape Condition
|z| > 2 (diverges)