Fractals

  1. Random and Stochastic Fractals
    1. Brownian Motion
      1. Mathematical Definition
        1. Properties and Characteristics
          1. Fractional Brownian Motion
            1. Hurst Exponent
            2. Percolation Theory
              1. Site Percolation
                1. Bond Percolation
                  1. Critical Thresholds
                    1. Infinite Clusters
                      1. Applications to Fractal Structures
                      2. Diffusion-Limited Aggregation
                        1. Growth Algorithm
                          1. Resulting Fractal Structures
                            1. Variations and Extensions
                              1. Physical Applications
                              2. Random Walk Models
                                1. Simple Random Walks
                                  1. Self-Avoiding Walks
                                    1. Lévy Flights
                                      1. Applications to Natural Phenomena
                                      2. Stochastic L-Systems
                                        1. Probabilistic Grammar Rules
                                          1. Plant Growth Modeling
                                            1. Branching Processes

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                                          6. Escape-Time Fractals

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                                          8. Fractals in Nature