Menger fractals


The Menger sponge is a fractal. It is a cube built up by smaller cubes and where a regular pattern of smaller cubes are removed. Each face of the sponge is a Sierpinski carpet, which is why the Menger sponge is sometimes also called a Sierpinski sponge. At each recursion step, the cubes with an edge on the edge of the larger cube from the previous iteration are kept.

image of a Menger sponge
The third iteration of a Menger sponge.

A Sierpinski-Menger snowflake is a variation to the Menger sponge. It is also a cube-based fractal but now eight corner cubes and the central cube are kept at each recursion step. This fractal can be thought of as a 3D analog of the Vicsek fractal.

image of a Menger flake
The third iteration of a Sierpinski-Menger snowflake.

This JavaScript web application animates a rotating 3D Menger sponge or flake. As a variation, you have the option to change the cubes into spheres.

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