Hausdorff Dimension Visualizer

Visualize and compare Hausdorff dimensions of classic fractals with interactive box-counting demonstrations.

Preview

Box-Counting Results

Grid Size	Box Count N(ε)	log(1/ε)	log(N)

Computed dimension: --

Controls

Fractal:

Fractal Depth: 4

Grid Divisions: 16

Show grid overlay

Stroke Color:

Line Width: 1

Background:

About the Hausdorff Dimension

Felix Hausdorff introduced the concept of fractal dimension in 1918. The Hausdorff dimension generalizes the notion of dimension beyond integers -- a line has dimension 1, a square has dimension 2, but fractals can have non-integer dimensions.

Box-Counting Method

The box-counting method approximates the Hausdorff dimension by counting how many boxes of size ε are needed to cover the fractal, then computing dim = lim(log N(ε) / log(1/ε)) as ε → 0. This visualizer lets you see the grid overlay and observe how the count scales.

Theoretical Dimensions

Koch curve: log(4)/log(3) ≈ 1.2619
Sierpinski triangle: log(3)/log(2) ≈ 1.5850
Cantor set: log(2)/log(3) ≈ 0.6309
Dragon curve: 2 (plane-filling)

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