This project centered on the visualization and exploration of the Calabi-Yau manifold—a complex, 6-dimensional space that plays a crucial role in string theory and theoretical physics. The objective was to understand, slice, and visualize this manifold in intuitive ways, allowing for better comprehension and appreciation of its intricate structure.
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Manifold Sampling:
- Developed functions to sample points from the Calabi-Yau manifold in 3D space.
- Introduced variations of the manifold sampling to explore different configurations and structures.
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2D Slicing:
- Sliced the 3D representation of the Calabi-Yau manifold into 2D cross-sections.
- Visualized the 2D slices' outlines, revealing the manifold's underlying structure at different depth levels.
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Enhanced 3D Visualization:
- Rendered the manifold in 3D with enhanced features, considering attributes like curvature and a mock Kähler potential.
- Used color mapping to display additional information on the manifold, aiding in-depth understanding.
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3D Reconstruction from 2D Slices:
- Extracted 2D slices from a provided GIF animation.
- Applied image processing techniques, including grayscale conversion, edge detection, and thresholding.
- Reconstructed and visualized the manifold in 3D from the processed 2D slices.
- Python Libraries: numpy, matplotlib, scipy, skimage, imageio.
- Visualization: 2D contour plots, 3D surface plots, 3D scatter plots, and wireframe plots.
The project succeeded in offering a multi-faceted view of the Calabi-Yau manifold, a structure that is notoriously difficult to visualize due to its higher-dimensional nature. Through systematic slicing, enhanced visualizations, and 3D reconstructions, we achieved a comprehensive exploration of the manifold's intricate patterns and attributes. This work serves as a foundation for further studies and visual explorations in the realm of theoretical physics and geometry.