Fractals

  1. Escape-Time Fractals
    1. The Escape-Time Algorithm
      1. Basic Algorithm Structure
        1. Iteration Limits
          1. Escape Criteria
            1. Optimization Techniques
            2. The Mandelbrot Set
              1. Mathematical Definition
                1. The Formula z → z² + c
                  1. Properties and Structure
                    1. Connectedness
                      1. Boundary Complexity
                        1. Self-Similarity at Different Scales
                        2. Notable Features
                          1. Main Cardioid
                            1. Period-2 Bulb
                              1. Seahorse Valley
                                1. Misiurewicz Points
                                2. Parameter Space Exploration
                                3. Julia Sets
                                  1. Definition and Construction
                                    1. Relationship to Mandelbrot Set
                                      1. Classification of Julia Sets
                                        1. Connected Julia Sets
                                          1. Disconnected Julia Sets
                                            1. Cantor Dust Julia Sets
                                            2. Parameter Dependence
                                              1. Filled Julia Sets
                                              2. Other Escape-Time Fractals
                                                1. Burning Ship Fractal
                                                  1. Tricorn (Mandelbar Set)
                                                    1. Newton Fractals
                                                      1. Newton's Method Application
                                                        1. Root-Finding Visualization
                                                          1. Basin Boundaries
                                                          2. Phoenix Fractals
                                                            1. Magnet Fractals

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                                                          5. Iterated Function Systems

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                                                          7. Random and Stochastic Fractals