Menger Sponge by Steve Plummer

Menger Sponge

Knitting
November 2015
Fingering (14 wpi) ?
28 stitches = 4 inches
US 2 - 2.75 mm
2187 yards (2000 m)
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This pattern is available for £4.50 GBP
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A Menger Sponge is a 3D fractal. Theoretically it has an infinite surface and zero volume.

If you take a 3 x 3 x 3 cube and remove the centre cube from each face and the very centre cube, you are left with 20 cubes. From each of these remove the centre cubes, as before, then keep on repeating this process. The surface area of the remaining shape keeps getting bigger and the volume keeps getting smaller.

The illusion representation disappears from view when you stand directly in front of it and you see only stripes.

The illusion could be made in any thickness of yarn but it is 290 stitches wide so using a thick yarn would make it very large. The hanging shown in the photos is about 105 cm (42”) square.