{"id":842,"date":"2017-09-05T08:30:36","date_gmt":"2017-09-05T12:30:36","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=842"},"modified":"2017-10-11T11:18:02","modified_gmt":"2017-10-11T15:18:02","slug":"sierpinski-carpet-2","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/05\/sierpinski-carpet-2\/","title":{"rendered":"Sierpinski Carpet"},"content":{"rendered":"

For my first fractal, I would love to try printing a Sierpinski Carpet. Not only am I beginner on the front of 3D printing, but I am also very fascinated by minimalist design. Illustrative Mathematics<\/a> states that this is a fractal whose area is zero, yet whose perimeter is infinite! Finding the perimeter can be solvable through exponential notation, though I do need to research more and understand why\/how that’s possible. In simpler terms, according to Wikipedia<\/a>, the Sierpinski Carpet is created by cutting a shape into 9 sub congruent equal squares, and then removing the middle square. This is a similar design technique to the Sierpinski Triangle, which involves a similar process but for triangles, or the Menger Sponge, a 3D cube version of the Sierpinski carpet.<\/p>\n

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I would like to try using this Sierpinski Carpet design<\/a>\u00a0by Chevron42 for my first print. Although the print may be a bit complicated and bigger (and I’d like to explore how I can minimize it), I think I can get it down to 50mm. Plus, it lends itself perfectly to dyeing, which would be perfect to use as a print for other things (wall decals, etc.)<\/p>\n