Fractals

9.

Applications of Fractal Geometry

9.1.

Computer Graphics and Visualization

9.1.1.

Procedural Terrain Generation

9.1.1.1.

Fractal Landscapes

9.1.1.2.

Mountain Range Modeling

9.1.1.3.

Realistic Coastlines

9.1.2.

Texture Generation

9.1.2.1.

Natural Surface Textures

9.1.2.2.

Procedural Materials

9.1.2.3.

Noise Functions

9.1.3.

Digital Art and Animation

9.1.3.1.

Fractal-Based Artworks

9.1.3.2.

Generative Design

9.1.3.3.

Interactive Visualizations

9.2.

Data Compression

9.2.1.

Fractal Image Compression

9.2.1.1.

Encoding Algorithms

9.2.1.2.

Decoding Processes

9.2.1.3.

Compression Ratios

9.2.1.4.

Quality Considerations

9.2.2.

Video Compression Applications

9.2.3.

Audio Signal Processing

9.3.

Engineering Applications

9.3.1.

9.3.1.1.

Fractal Antenna Geometry

9.3.1.2.

Multiband Performance

9.3.1.3.

Size Reduction Benefits

9.3.2.

Heat Transfer Enhancement

9.3.2.1.

Fractal Heat Exchangers

9.3.2.2.

Surface Area Optimization

9.3.3.

Materials Science

9.3.3.1.

Porous Material Analysis

9.3.3.2.

Surface Roughness Characterization

9.3.3.3.

Composite Material Design

9.4.

Medical and Biological Applications

9.4.1.

Medical Imaging Analysis

9.4.1.1.

Tumor Growth Modeling

9.4.1.2.

Organ Structure Analysis

9.4.1.3.

Blood Vessel Network Analysis

9.4.2.

Physiological Signal Analysis

9.4.2.1.

Heart Rate Variability

9.4.2.2.

EEG Pattern Analysis

9.4.2.3.

Respiratory Pattern Studies

9.4.3.

Drug Delivery Systems

9.4.3.1.

Fractal Pharmacokinetics

9.4.3.2.

Targeted Delivery Mechanisms

9.5.

Financial and Economic Modeling

9.5.1.

Market Volatility Analysis

9.5.2.

Price Movement Patterns

9.5.3.

Risk Assessment Models

9.5.4.

Fractal Market Hypothesis

9.5.5.

Portfolio Optimization

9.6.

Urban Planning and Geography

9.6.1.

City Growth Modeling

9.6.2.

Transportation Network Analysis

9.6.3.

Population Distribution Studies

9.6.4.

Land Use Pattern Analysis

9.6.5.

Infrastructure Planning

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8. Fractals in Nature

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10. Connections to Related Fields