The Sierpiński carpet is a beautiful fractal, a shape that contains itself in infinitely many smaller and smaller copies. Its area is 0 and dimension is log(8)/log(3) ≈ 1.8928.
You can make a Sierpiński carpet in "3 simple steps":
Step 1) Take a square and divide it into 9 smaller squares of equal size.
Step 2) Cut out the square in the middle.
Step 3) Repeat steps 1 and 2 each of the smaller squares.
Here is the carpet after the first two iterations.
Step 1) Take a square and divide it into 9 smaller squares of equal size.
Step 2) Cut out the square in the middle.
Step 3) Repeat steps 1 and 2 each of the smaller squares.
Here is the carpet after the first two iterations.
The 3D version is called the Menger sponge. We have a couple of them here @mathsleedsuni. People use them as coffee tables. ☕ #maths #fractal
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