Making-Scientific-Visualizations-with-the-Omniacs
📈 3D Normal Distribution Visualization with Manim
This project animates the bivariate normal distribution as a 3D surface using Manim. It includes interactive elements like rotating camera views, contour plots, cross-sections, and annotated explanations — perfect for statistics and machine learning education.
🧠 What It Teaches
- Shape and symmetry of the 2D Gaussian distribution
- Probability density visualization in 3D
- Contour lines representing equal-probability curves
- Cross-sectional normal distributions along fixed y-values
📊 Visual Features
| Element | Description |
|---|---|
| 📉 3D Surface | Bell-shaped Gaussian surface defined by P(x,y) = e^(-((x²+y²)/2)) / (2π) |
| 🎯 Contours | Level curves for constant probability heights |
| 🔴 Cross Sections | Horizontal slices showing 1D normal distributions |
| 🎥 Camera Motion | Ambient rotation and zoom views |
| 🖋️ Annotations | Title, math function, and inline explanations |
| 🎨 Color Mapping | Gradients, checkerboards, and custom contour colors |
📦 Requirements
- Python 3.8+
- Manim Community Edition
- NumPy
- SciPy
pip install manim numpy scipy
▶️ How to Run
manim -pql Normal_distribution.py ComprehensiveNormalDistribution3D
Use -qh for high-resolution output. 📁 Files
Normal_distribution.py — Full Manim animation logic
README.md — This file
🎓 Ideal For
Teaching statistical distributions
Demonstrating machine learning fundamentals
Data visualization education
Interactive math explainer videos
🤝 Support Visual Math Education
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