🧪 Mathematics Fractals Simulation

Explore fractal structures and their properties by adjusting parameters: this simulation builds a genuine three-dimensional Cantor set by repeatedly splitting a cube into 27 equal sub-cubes and keeping only the 8 corners, discarding the other 19 pieces at every generation. The result is "dust" — a totally disconnected point-cloud whose self-similarity dimension D = ln(8)/ln(3) ≈ 1.893 is fixed by the construction rule itself and stays constant no matter how deep the recursion runs. Drag the iteration-depth slider to rebuild the cloud from 1 cube up to 32,768 GPU-instanced cubes, pull the gap-spacing slider to separate the recursive clusters and see the corner-only rule at every scale, and switch between coloring by octant lineage or by radial shell.