Box-Counting Fractal Dimension Estimator (2D)

This simulator runs the box-counting algorithm — the workhorse of computational pattern-complexity analysis — on four different 2D point sets live in your browser. Choose a pattern (a chaos-game Sierpinski triangle, a 2D Cantor dust, a uniform random cloud, or a thin line confined inside the plane), and the scene overlays a square grid at six scales, counting how many cells each pattern touches at every scale. A live log-log regression panel plots log N(s) against log(1/s) and turns those six points into a single number, the estimated fractal dimension D, updating as you regenerate the pattern, change its point density, or drag/zoom your view of the plane — letting you watch a genuinely algorithmic pattern-recognition measurement converge toward each shape's known theoretical dimension.