Part VI: Interactive Applications¶

This work is licensed under a Creative Commons Attribution 4.0 International License.

This section provides access to interactive tools and demonstrations for exploring fractal mathematics and self-affine patterns. The applications are implemented in two frameworks:

React Applications: High-performance web applications with GPU-accelerated visualization
Streamlit Applications: Python-based interactive tools for scientific exploration

Available Tools¶

Fractal Visualizations¶

Application	Framework	Description
Mandelbrot Explorer	React	Interactive Mandelbrot set visualization with zoom and parameter controls
Julia Set Explorer	React	Real-time Julia set rendering with adjustable complex parameter
DLA Simulator	React	Diffusion Limited Aggregation growth simulation
Barnsley Fern	React	IFS-based fern generation

Tree and Branching Architectures¶

Application	Framework	Description
Pythagoras Tree	React	Self-similar tree with adjustable branching angle
L-System Trees	React	Lindenmayer system-based tree generation
3D Tree/Root Visualization	React	Three-dimensional branching network visualization

3D Simulation & Rendering¶

Application	Framework	Description
Blender DLA	Blender/Python	3D DLA simulation with Geometry Nodes and Cycles rendering

Analysis Tools¶

Application	Framework	Description
Differential Box-Counting	Python	Calculate fractal dimensions of grayscale images
Noise Generators	React	1/f noise and fractional Brownian motion

Mathematical Visualizations¶

Application	Framework	Description
Riemann Zeta 2D	React	2D visualization of the Riemann zeta function
Riemann Zeta 3D	React	3D surface plot of zeta function magnitude

Quick Start¶

Running React Applications¶

The React applications are deployed and accessible online:

Launch Interactive Apps

Or run locally:

cd react
npm ci
npm start

Running Streamlit Applications¶

cd apps
pip install -r requirements.txt
streamlit run mandelbrot.py

Technical Requirements¶

For React Applications¶

Modern web browser with WebGL support
JavaScript enabled
Recommended: Chrome, Firefox, or Safari

For Python Applications¶

Python 3.8+
NumPy, SciPy, Matplotlib, Plotly
Streamlit (for interactive apps)
See Installation Guide for full setup

Application Architecture¶

graph TB
    subgraph React["React Applications"]
        R1[Mandelbrot/Julia] --> WebGL
        R2[DLA/Trees] --> Canvas2D
        R3[Zeta Functions] --> Plotly
    end

    subgraph Python["Python Applications"]
        P1[Streamlit Apps] --> Matplotlib
        P1 --> Plotly
        P2[Jupyter Notebooks] --> NumPy
    end

    subgraph Blender["Blender Applications"]
        B1[DLA Simulation] --> GeometryNodes
        B2[Cycles Rendering] --> GPU2[GPU Rendering]
    end

    WebGL --> GPU[GPU Acceleration]
    Canvas2D --> CPU[CPU Rendering]
    GeometryNodes --> GPU2

Contributing¶

To add new applications or improve existing ones:

React apps: Add new pages to react/src/pages/
Streamlit apps: Add new .py files to apps/
Follow the existing code patterns for consistency
Include documentation in this section