Fractals (Art to Applied Science)
This text is a reference for learning and mastering fractals (theoretical and applied perspective). In these pages, we provide links to official code and documentation, discuss how the fractal algorithms function, present code examples in editable sandboxes with explanations.
Copyright © 2023 Benjamin Kenwright.
The code for this book was developed by Benjamin Kenwright and is licensed under the MIT license.
The cover art was created by Benjamin Kenwright and is based on a fractal example from the text.
Special thanks to reviewers, colleagues and friends for input and discussion while developing the initial versions of the text.
Contents
Chapter 1: Introduction to Fractals
- What are Fractals?
- Brief History of Fractals
- Fractal Dimensions
- Why Study Fractals?
- Fractal Misconceptions and Myths
- Fractal Examples
Chapter 2: Fractal Geometry
- Iterated Function Systems (IFS)
- Fractal Sets and Spaces
- The Mandelbrot Set
- The Julia Set
- Self-Similarity and Scaling
Chapter 3: Fractal Applications
- Fractal Analysis of Natural Phenomena
- Fractal Art and Music
- Fractal Compression and Encryption
- Fractal Terrain and Landscape Generation
- Fractal Modeling of Economic and Social Systems
Chapter 4: Fractal Algorithms and Techniques
- Chaos Theory and Strange Attractors
- Random Fractals and Brownian Motion
- Fractal Interpolation and Extrapolation
- Fractal Dynamics and Optimization
- Fractal Monte Carlo and Quasi-Monte Carlo Methods
Chapter 5: Fractal Software and Tools
- Fractal Generation Software
- Fractal Visualization and Animation
- Fractal Image and Signal Processing
- Fractal Data Analysis and Classification
- Fractal Programming Languages and Libraries
- Fractal Critique and Evaluation
Chapter 6: Fractal Challenges and Future Directions
- Unsolved Problems in Fractal Theory
- Fractal Complexity and Computation
- Fractal Ethics and Sustainability
- Fractal Education and Outreach
- Fractal Collaborations and Communities.
Chapter 7: Fractal Variations and Extensions
- Fractional Calculus and Fractal Derivatives
- Multifractals and Singularity Analysis
- Hierarchical Fractals and Nested Structures
- Quantum Fractals and Chaos
Chapter 8: Fractal Connections and Contexts
- Fractals and Physics
- Fractals and Biology
- Fractals and Neuroscience
- Fractals and Economics
- Fractals and Philosophy
Chapter 9: Fractal Experiments and Projects
- Building Fractal Sculptures and Installations
- Designing Fractal Patterns and Fabrics
- Creating Fractal Music and Sounds
- Writing Fractal Poetry and Literature
- Developing Fractal Games and Apps