Three visualizations exploring the 2023 mathematical discovery of the "Einstein Hat" - a single tile that covers the plane infinitely without ever repeating.
Here are some images of the animations I created:
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| 1. The Einstein Hat Story | 2. Kaleidoscopic Tree of life | 3. Butterfly Rorschach |
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| 4. Kaleidoscopic Flower of Life | 5. Mandala Visualization | 6. Spirograph Pattern |
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| 7. Sri Yantra |
"The Puzzle That Whispered to Infinity"
500 tiles emerge one-by-one in a hexagonal spiral, revealing how a single aperiodic shape grows into infinite non-repeating patterns. Five narrative chapters guide the viewer through the mathematical journey.
Output: einstein_hat_story.mp4 (500 frames, 80ms intervals)
einstein_hat_story.mp4
"Sacred Geometry Meets Aperiodicity"
Einstein Hat tiles compose a fractal tree structure with recursive branching. Chakra-inspired colors pulse through generations, merging sacred geometry's symmetry with mathematical aperiodicity.
Output: kaleidoscope_fractal_tree_4K.mp4 (42 frames, 4K quality)
kaleidoscope_fractal_tree_4K.mp4
"Symmetry from Chaos"
A perfectly symmetric butterfly emerges through simulated ink diffusion on paper. The animation explores the tension between bilateral symmetry and organic randomness, reminiscent of psychological inkblot tests.
Output: butterfly_rorschach.mp4 (120 frames, ink spreading effect)
butterfly_rorschach.mp4
In March 2023, mathematicians discovered a 13-sided polygon that:
✅ Tiles the entire plane (no gaps, no overlaps)
✅ Never creates a repeating pattern (aperiodic)
✅ Requires only one tile shape (monotile)
This solved the decades-old "einstein problem" (ein stein = German for "one stone").
Why it matters: Previous aperiodic tilings needed multiple tile types (like Penrose tiles). The Einstein Hat does it alone.
- Custom geometry engine: Rotation matrices, hexagonal spirals, recursive fractals
- PlotnineAnimation: Frame-by-frame control with
interval,dpi=300,bitrate=12000 - Data-driven color: Pre-computed colors/alphas mapped to tile generations
- Performance: Vectorized NumPy operations handling 6000+ tiles across 500 frames
(ggplot(aes('x', 'y', group='tile_id', fill='color'))
+ geom_polygon() # Closed shapes from vertices
+ scale_fill_identity() # Pre-calculated colors
+ coord_equal() # Undistorted geometry
+ theme_void()) # Clean mathematical aestheticpip install plotnine pandas numpy matplotlibOpen 2025_Plotnine_Contest.ipynb and run cells sequentially. Each visualization is independent:
- Einstein Hat Story (~2 min, 500 frames)
- Fractal Tree (~90 sec, 42 frames)
- Butterfly Rorschach (~60 sec, 120 frames)
├── 2025_Plotnine_Contest.ipynb # Main notebook with all three visualizations
├── README.md # This file
├── output_animations/ # Folder for all output files
│ ├── einstein_hat_story.mp4 # Output animation 1
│ ├── kaleidoscope_fractal_tree_4K.mp4 # Output animation 2
│ └── butterfly_rorschach.mp4 # Output animation 3
├── output_images/ # (Optional) For thumbnails
Each visualization explores a different aspect of the Einstein Hat:
- Story: Narrative emergence - how patterns grow without repeating
- Tree: Structural beauty - aperiodicity meets natural fractals
- Butterfly: Psychological paradox - forcing symmetry onto chaos
- 🎨 Color palettes: Earth tones, chakra spectrum, aged paper
- 🖤 Dark backgrounds: Cosmic depth for mathematical meditation
- ⚡ Animation timing: Slow enough to observe, fast enough to engage
- 📐 Square compositions: Respect geometric integrity
Mathematical Source:
- Smith, D., et al. (2023). "An aperiodic monotile". arXiv:2303.10798
Visualization Inspiration:
- Dimensionality Reduction Animated by Jeroen Janssens
- My 2024 Plotnine Contest Entry
Author: Jaspreet Pabla | Year: 2025 | Contest: Plotnine Data Storytelling
"In the end, I discovered that infinity doesn't repeat—it evolves."
- GitHub: [Your GitHub Profile]
- Contest Discussion: [Contest Discussion Page]
License: MIT (code) | CC-BY-4.0 (visualizations)