Fractal dimension simulation

A simple random rule makes the Sierpiński gasket — how much of the plane does it fill?

▶ Run the simulationSee the measured result

Units: dimensionless (box-counting dimension of the Sierpinski gasket, exactly log 3 / log 2; secondary knowns: filled square D = 2 exact, similarity law D(r) = log 3 / log(1/r), uniform cloud D = 2)

How the lab tests it

Run the chaos game (jump halfway to a random triangle corner), then box-count: cover the plane with boxes of side ε, count occupied boxes N(ε), and fit the slope of log N vs log(1/ε).

What it checks

the exact Hausdorff dimension D = log 3 / log 2 ≈ 1.585 (between a line and an area)