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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
Connections to Related Fields
Chaos Theory
Sensitive Dependence on Initial Conditions
The Butterfly Effect
Lyapunov Exponents
Strange Attractors
Lorenz Attractor
Rössler Attractor
Hénon Attractor
Routes to Chaos
Period-Doubling Cascades
Intermittency
Crisis Events
Dynamical Systems Theory
Phase Space Analysis
Bifurcation Theory
Stability Analysis
Poincaré Maps
Hamiltonian Systems
Cellular Automata
Rule-Based Systems
Conway's Game of Life
Elementary Cellular Automata
Fractal Patterns in CA
Self-Organization Principles
Information Theory
Algorithmic Information Theory
Kolmogorov Complexity
Entropy and Fractals
Data Compression Connections
Statistical Physics
Critical Phenomena
Phase Transitions
Scaling Laws
Renormalization Group Theory
Percolation Theory
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9. Applications of Fractal Geometry
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11. Computational Methods and Tools