Famous Fractals
Sierpinski Carpet
Sierpinski Carpet is an example of a fractal cluster, which can be formed by cutting out parts of a 2-dimensional figure. The Sierpinski Carpet starts with a square, which is divided into 9 smaller squares, and cuts out the center square:
After that the same is done with each of the 8 squares left:
If you continue the process infinitely, you will get the Sierpinski Carpet:
FRACTAL DIMENSION
In the fractal, there are 8 identical figures, each of which has to be magnified 3 times to get the entire figure. Using the similarity method, we can find the fractal dimension to be log 8 / log 3, which is approximately 1.89.
AREA
After every iteration, we leave 8/9 of the area of the figure. To find the area of the figure after some number of iterations, we have to raise 8/9 to the power of that number. Although it doesn’t seem so, after an infinite number of iterations, the area will become 0.
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