Emergent Impossible Fractal Geometry
A 4-State Cellular Automaton on Triangular Tessellations
A 4-state cellular automaton with 78 transition rules over a 7-cell neighborhood. When rendered on a triangular tessellation, its output is perceived as impossible 3D fractal geometry under isometric projection. Among its outputs is the Selmi triangle, a fractal Penrose tribar with self-similar structure at every scale.
Presets: The original rule set is Selmi (2009), producing the fractal Penrose tribar. Kitaoka 2010 and Selmi (2019) are variants with different beam crossing behavior. Right Stairs produces a descending staircase of impossible cubes. The remaining presets generate non-interacting geometric primitives (single beams, cubes, ladders).
How to use:
Press Generate to run the automaton.
Edit the Init string to change the seed (W=white, R=red, G=green, B=blue).
Adjust Rows to control evolution depth.
Hover over any triangle to inspect its neighborhood and matching rule.
Click a triangle to load its rule into the editor.
Use Export to download the output as SVG.