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.
This system starts with a 2×2 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.
- 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.
You are looking at:
- Recursive permutations
- Lossless symbolic expansion
- Fractal geometry with digital DNA
This is the cleanest chaos you’ll ever see.
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MIT License. See LICENSE for details.
Serhii Herasymov