BETWEEN DIMENSIONS
Box counting
Cover a shape with boxes of side ε and count N(ε), the number that touch the shape. If N scales approximately like ε−D, the slope estimates a box-counting dimension.
D ≈ − slope of log N(ε) vs log ε
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Classic values
| Fractal | Dimension |
|---|---|
| Cantor set | 0.63093 |
| Koch curve | 1.26186 |
| Sierpiński triangle | 1.58496 |
| Sierpiński carpet | 1.89279 |
| Menger sponge | 2.72683 |
| Mandelbrot boundary | 2 (Hausdorff) |