/building · 2018
Gingerbread Menger Cube
fractal · edible · holiday
Six gingerbread Sierpinski carpets assembled with royal icing into a Menger cube, built to get relatives asking about fractals over the holidays.
Take a square, cut it into a three by three grid, remove the middle one, and repeat on the eight that are left. That's a Sierpinski carpet. Do the same thing to a cube, in three dimensions, and you get a Menger sponge, which loses volume with every iteration while its surface area grows without bound.
Each face is a level-two carpet, which is one large square hole surrounded by eight small ones. Cutting them is the easy part. Getting six panels of gingerbread with that much material removed to stand up as a cube is not, and royal icing turns out to be the right adhesive because it sets hard rather than staying tacky.
The real appeal is that it is a very good conversation object. It sits on a kitchen counter over the holidays, someone asks what the holes are for, and you get to explain that this is what a Cantor set looks like if you do it to a cookie. Nobody escapes the room without hearing about limiting volume.