Menger Sponge: Fractal Dimension

This video continues with the Menger Sponge, a fractal named after the Austrian American mathematician Karl Menger, and specifically focuses on finding the fractal dimension of the object.
The fractal is created by starting with a cube, dividing the cube into 27 equally sized smaller cubes, and removing the middle cube on each of the 6 faces as well as the cube from the center, leaving 20 of the original 27 cubes. This process is then repeated for each of the remaining 20 cubes and so on.
When this process is carried out infinitely manner times, the Menger Sponge is created. This fractal has dimension approximately equal to 2.73 and has infinite surface area but the volume is equal to zero.
EulersAcademy.org

[@TesserId]

It's interesting that the program I use, which is really a game engine (Sauerbraten), allows copy and past with automatic resize. That means that after I poke the first set of holes through, I make a copy of the overall cube and then set the paste size, and paste each of the next smaller positions. That can then be repeated recursively.

[@EulersAcademy]

Thanks for watching. That's pretty interesting. Fractals work great with various computer programs.