perfect-shuffle
🧠Perfect Shuffle Fractals
Translated Article (Engilsh)
Original Article (Russian language)
These aren’t your average fractals.
What you see here is the result of a brutally simple idea:
Take a tiny grid, and recursively expand it using fixed spatial permutations.
No randomness.
No equations.
Just pure, symbolic structure — repeated through perfect, rule-based subdivision.
And the result?
Fractals that look like logic itself folding in on itself.
⚙️ What’s going on?
This system starts with a 2Ă—2 binary grid. On each iteration:
- The grid doubles in size
- Each
2×2block is filled based on the current rule set - These rules are just perfect shuffles — deterministic rearrangements of pixel positions
You can think of each rule as a spatial bitwise operation.
The result is a massive, recursively structured pattern, built from nothing but clean logic.
🔥 Why it’s crazy cool
- Perfect self-similarity — no noise, no decay
- Recursive logic — every pixel is a decision made by a rule, not a formula
- Unreasonably expressive — despite the rules being tiny integers (
0–15), the patterns explode into complexity - Visual proofs — each image is a pure mathematical artifact
These aren’t just visualizations. They’re symbolic systems unfolding.
They’re the cousin of cellular automata and convolutional networks — but sharper, more discrete, and infinitely interpretable.
🧪 TL;DR
You are looking at:
- Recursive permutations
- Lossless symbolic expansion
- Fractal geometry with digital DNA
This is the cleanest chaos you’ll ever see.
Gallery
| Â | Â | Â |
|---|---|---|
| 2.1.15.14 grey | 2.1.15.14 rgb | 2.1.15.14 binary |
 |
 |
 |
| 6.14.0.0 grey | 6.14.0.0 rgb | 6.14.0.0 binary |
 |
 |
 |
| 9.4.0.11 grey | 9.4.0.11 rgb | 9.4.0.11 binary |
 |
 |
 |
| 4.8.4.7 grey | 4.8.4.7 rgb | 4.8.4.7 binary |
 |
 |
 |
| 13.14.0.3 grey | 13.14.0.3 rgb | 13.14.0.3 binary |
 |
 |
 |
| 14.1.11.10 grey | 14.1.11.10 rgb | 14.1.11.10 binary |
 |
 |
 |
| 4.13.15.0 grey | 4.13.15.0 rgb | 4.13.15.0 binary |
 |
 |
 |
| 15.6.8.3 grey | 15.6.8.3 rgb | 15.6.8.3 binary |
 |
 |
 |
| 4.0.2.14 grey | 4.0.2.14 rgb | 4.0.2.14 binary |
 |
 |
 |
| 5.0.2.15 grey | 5.0.2.15 rgb | 5.0.2.15 binary |
 |
 |
 |
| 2.0.2.9 grey | 2.0.2.9 rgb | 2.0.2.9 binary |
 |
 |
 |
| 14.3.1.0 grey | 14.3.1.0 rgb | 14.3.1.0 binary |
 |
 |
 |
| 4.1.11.8 grey | 4.1.11.8 rgb | 4.1.11.8 binary |
 |
 |
 |
| 10.0.3.0 grey | 10.0.3.0 rgb | 10.0.3.0 binary |
 |
 |
 |
đź“„ License
MIT License. See LICENSE for details.
👤 Author
Serhii Herasymov
sergeygerasimofff@gmail.com
https://github.com/xcontcom