Fractional Dimensions — Mathematics

Menger spongeHausdorff dimension = log(20) / log(3) ≈ 2.727

Rule

Switch squares on or off. Repeat that same choice inside every retained square.

Dimension2.727

01234

Iteration2

Expand0%

4D slice04D turn20°

Scroll to zoom toward the center, or start a zoom journey. Drag to rotate; right-drag to pan.

Detail3 / 5

Position0 Tilt25° Turn20°

Both halves keeps the object together and marks the cut. Cross-section shows only the shape where the cut passes.

ShapeSquareDivisions3Variation1

Mathematical construction · original = 100%

Amount12%