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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
12.
Advanced Topics and Current Research
12.1.
Fractal Calculus
12.1.1.
Fractional Derivatives
12.1.2.
Fractional Integrals
12.1.3.
Applications to Fractal Functions
12.2.
Quantum Fractals
12.2.1.
Quantum Mechanics on Fractal Structures
12.2.2.
Fractal Quantum Systems
12.2.3.
Quantum Chaos Connections
12.3.
Fractal Networks
12.3.1.
Scale-Free Networks
12.3.2.
Small-World Networks
12.3.3.
Network Topology Analysis
12.3.4.
Social Network Applications
12.4.
Machine Learning and Fractals
12.4.1.
Fractal Feature Extraction
12.4.2.
Pattern Recognition Applications
12.4.3.
Neural Network Architectures
12.4.4.
Deep Learning on Fractal Data
12.5.
Experimental Fractal Research
12.5.1.
Laboratory Fractal Generation
12.5.2.
Physical Fractal Systems
12.5.3.
Measurement Techniques
12.5.4.
Validation of Theoretical Models
12.6.
Interdisciplinary Applications
12.6.1.
Fractal Ecology
12.6.2.
Fractal Psychology
12.6.3.
Fractal Architecture
12.6.4.
Fractal Music and Art Theory
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11. Computational Methods and Tools
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1. Introduction to Fractals