29 May 2014

FRACTAL MENGER SPONGE

A lot of students at Amara Berri school  are building a great Menger sponge, made of 8,000 little cubes. Here you have an image to see one.
When they have finished we will take a photo to show you the result.

KEEP GOING KIDS AND TEACHERS!!!

Loop Menger animated GIF
http://giphy.com/search/menger-sponge






Here we have an example of a second iteraction but it can be much bigger...


























How it is constructed

According to Wikipedia, the construction of a Menger sponge can be described as follows:
1. Begin with a cube.
2. Divide every face of the cube into 9 squares, like a Rubik's Cube. This will sub-divide the cube into 27 smaller cubes.
3. Remove the smaller cube in the middle of each face, and remove the smaller cube in the very center of the larger cube, leaving 20 smaller cubes. This is a level-1 Menger sponge (resembling a Void Cube).
4. Repeat steps 2 and 3 for each of the remaining smaller cubes, and continue to iterate ad infinitum.
The second iteration will give you a level-2 sponge, the third iteration gives a level-3 sponge, and so on. The Menger sponge itself is the limit of this process after an infinite number of iterations.


FINAL RESULTS





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