{"id":721,"date":"2017-09-04T15:44:48","date_gmt":"2017-09-04T19:44:48","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=721"},"modified":"2017-10-11T11:19:00","modified_gmt":"2017-10-11T15:19:00","slug":"menger-sponge","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/04\/menger-sponge\/","title":{"rendered":"Menger Sponge"},"content":{"rendered":"

According to Wikipedia<\/a> the Menger Sponge is a 3 Dimensional fractal curve. It \u00a0was first described by Karl Menger in 1926. To create a Menger Sponge you start with a cube. The face of a Menger Sponge is a\u00a0Sierpinski carpet, a 2 dimensional fractal. Every face of the cube is then divided into 9 squares. Wikipedia compares a level 1 Menger Sponge to a Rubik’s Cube. The next step would be to remove the smaller cube in the middle of each face, and remove the smaller cube in the very center of the larger cube. These steps can be repeated infinitely.<\/p>\n

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I liked this animation of the progression of a Menger Sponge. It goes from a simple cube to a extremely complex fractal. The Menger Sponge is considered a fractal because it is a universal curve. I’m not entirely sure what that means but I believe since the same shape is repeatedly divided that makes it a fractal.<\/p>\n