Box-Counting Fractal Dimension Estimator

This simulator runs the box-counting algorithm — the workhorse of computational pattern-complexity analysis — on four different 3D point clouds live in your browser. Choose a pattern (a chaos-game Sierpinski tetrahedron, a 3D Cantor dust, a uniform random cloud, or a flat plane), and the scene overlays a cubic grid at six scales, counting how many cells each pattern touches at every scale. A least-squares fit of log N(s) against log(1/s) turns those counts into a single number, the estimated fractal dimension D, updated live as you regenerate the pattern or change its point density — letting you watch a genuinely algorithmic pattern-recognition measurement converge toward each shape's known theoretical dimension.