Box-Counting Log-Log Scaling · DLA · Sierpiński · Cantor
The sandbox (box-counting) method covers the fractal with boxes of size ε and counts N(ε) occupied boxes. The fractal dimension D_f = −lim_{ε→0} log N(ε)/log ε appears as the slope of the log-log plot. Compare measured D_f to theoretical values: Sierpiński = log3/log2 ≈ 1.585, Cantor dust ≈ 1.26, DLA ≈ 1.71, Koch ≈ 1.26.