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Mathematics
Fractals
1. Introduction to Fractals
2. Mathematical Foundations
3. Fractal Dimension
4. Classical Fractals
5. Iterated Function Systems
6. Escape-Time Fractals
7. Random and Stochastic Fractals
8. Fractals in Nature
9. Applications of Fractal Geometry
10. Connections to Related Fields
11. Computational Methods and Tools
12. Advanced Topics and Current Research
10.
Connections to Related Fields
10.1.
Chaos Theory
10.1.1.
Sensitive Dependence on Initial Conditions
10.1.2.
The Butterfly Effect
10.1.3.
Lyapunov Exponents
10.1.4.
Strange Attractors
10.1.4.1.
Lorenz Attractor
10.1.4.2.
Rössler Attractor
10.1.4.3.
Hénon Attractor
10.1.5.
Routes to Chaos
10.1.5.1.
Period-Doubling Cascades
10.1.5.2.
Intermittency
10.1.5.3.
Crisis Events
10.2.
Dynamical Systems Theory
10.2.1.
Phase Space Analysis
10.2.2.
Bifurcation Theory
10.2.3.
Stability Analysis
10.2.4.
Poincaré Maps
10.2.5.
Hamiltonian Systems
10.3.
Cellular Automata
10.3.1.
Rule-Based Systems
10.3.2.
Conway's Game of Life
10.3.3.
Elementary Cellular Automata
10.3.4.
Fractal Patterns in CA
10.3.5.
Self-Organization Principles
10.4.
Information Theory
10.4.1.
Algorithmic Information Theory
10.4.2.
Kolmogorov Complexity
10.4.3.
Entropy and Fractals
10.4.4.
Data Compression Connections
10.5.
Statistical Physics
10.5.1.
Critical Phenomena
10.5.2.
Phase Transitions
10.5.3.
Scaling Laws
10.5.4.
Renormalization Group Theory
10.5.5.
Percolation Theory
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9. Applications of Fractal Geometry
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11. Computational Methods and Tools