Fractal Dimension: Between Curve and Plane

The Sierpinski triangle has dimension 1.585 — too jagged to be a curve, too sparse to fill a plane.

Controls

3
0.500
d = log(N) / log(1/s)
  = log(3) / log(2.000)
d = 1.585

Gallery

Fractal (4 iterations, IFS)

Box Counting

Slope of log-log plot ≈ fractal dimension d

Red line: slope = d

Iteration Depth

4 levels (fixed)