The Menger Sponge, a well-studied fractal, was first described in the 1920s. The fractal is cube-like, yet its cross section is quite surprising. What happens when it is sliced on a diagonal plane? Try to predict the solution to the puzzle proposed in this video.

References:

The Menger Sponge (Wikipedia page)

Photo by Sébastien Pérez-Duarte

Related:

More videos from the Mathematical Impressions series.

Very nice! Could you give some detail on how you made the model (e.g. which 3D printer and software you used, any tips, etc.)? Thanks.

Simply beautiful! mathematics and universal order reveling each other (at least this is how I see it).

Great work

heh, my first instinctive guess was correct, but then I decided it couldn’t be the right answer because it wasn’t “surprising”, and I rationalized my way to a wrong answer.

Simplemente genial, ¡maravilloso! Tengo una pregunta, ¿en qué programa se hizo la simulación? Gracias.

Nice! I would also like to know what 3D printer you used and a link to the file since I have my own Replicator 1 which I would like to attempt this on.

To answer some of these questions: I used at least a half dozen software tools in generating the animations and the 3D models, including Mathematica, Maya, and Rhinoceros.

I fabricated the 3D-printed models by selective laser sintering on a DTM2500+ machine at Stony Brook University, but other high-resolution machines are equally capable of producing such models. If you have access to a 3D printer, the stl file for the sliced 3rd-order Menger sponge can be downloaded from here:

http://georgehart.com/rp/rp.html

It’s amazing like everything you do …

A big hug from southern Europe,

Clara

Fantastic!! Congratulations.

I’m not sure when I came up the the same results in Sketchup, It may have been even before 2007. But I’m not a studied mathematician or someone in the science field. I figure if someone like me found this, a professor or even a grad student would have already found it. Shows that discovery can come from anyplace.

Very interesting. I have seen this in a mo-math presentation but this helped me understand it more. Everyone I know who has seen this was amazed. Amazing!!

This is utterly superb work!! Problem is, you have now cost me a lot of money as I now have to go out and buy a 3D printer. I have wanted to do precisely this sort of thing for a few years now but when I looked at this around 5 years ago it was nowhere near as advanced as it is now. First project for me will be to see if I can print out a Roman surface.

I teach an Introduction to Fractals and Chaos course eery other year to secondary math teachers. The in-between years I look for new twists on the stable content in the course and your video brings a fresh and exciting extension to the Menger Sponge. Thanks!