An interactive 3D fractal visualization tool for exploring the fascinating Mandelbulb fractal in real-time.

The Mandelbulb Explorer is a Python-based application that allows users to visualize and interact with the Mandelbulb, a three-dimensional analog of the Mandelbrot set. This tool enables real-time manipulation of fractal parameters, providing an intuitive way to explore the complex and beautiful geometry of this mathematical object.

• Interactive Visualization: Rotate, zoom, and explore the 3D fractal in real-time
• Parameter Adjustment: Modify power, resolution, and iteration values on-the-fly
• GPU Acceleration: Utilizes Numba for high-performance parallel computing
• Animation Support: Built-in rotation animation for captivating visualizations

The Mandelbulb is a three-dimensional fractal, constructed through an iterative formula similar to the Mandelbrot set but extended to three dimensions. For each point (x,y,z) in 3D space, the formula iterates:

(x,y,z) → (r^n * sin(n*θ) * cos(n*φ) + x₀, r^n * sin(n*θ) * sin(n*φ) + y₀, r^n * cos(n*θ) + z₀)

Where:

• r is the radius in spherical coordinates
• θ (theta) is the polar angle
• φ (phi) is the azimuthal angle
• n is the power parameter (typically 8 for the classic Mandelbulb)

Points that remain bounded after iterations belong to the set and are colored according to how quickly they escape.

• Python 3.7 or higher
• pip (Python package installer)

1. Clone the repository:

   git clone https://github.com/yourusername/mandelbulb-explorer.git
   cd mandelbulb-explorer
   

2. Create a virtual environment (optional but recommended):

   python -m venv venv
   source venv/bin/activate  # On Windows, use: venv\Scripts\activate
   

3. Install dependencies:

   pip install numpy matplotlib numba
   

Run the explorer:

python mandelbulb_explorer.py

• Arrow Up/Down: Increase/decrease power value
• +/-: Increase/decrease resolution
• [/]: Increase/decrease maximum iterations
• Mouse: Rotate the view (when animation is paused)
• Spacebar: Pause/resume animation (not implemented in current version)

• Higher resolution values and iteration counts will require more computational resources
• First-time execution includes a JIT compilation step, which may cause a brief delay
• For optimal performance, a computer with a multi-core CPU is recommended

You can modify the following parameters in the code:

• Initial power value (default: 8.0)
• Initial resolution (default: 50)
• Initial max iterations (default: 20)
• Color map (default: 'plasma', alternatives: 'viridis', 'inferno', etc.)
• Point size (default: 15)

Potential improvements for future versions:

• Support for different fractal types
• Color customization interface
• Direct export of high-resolution images
• Virtual reality support
• Improved camera controls
• Custom slicing planes

This project was inspired by:

• Daniel White's original Mandelbulb formulation
• Various mathematical visualizations from the fractal community

Mathio M.Luca - luca.mathio1@gmail.com