Project a - Fractal dimension of the Cantor gasket

The Cantor gasket is built up with small squares of side, say, 1cm, as shown below (see, Lesson 5)

You first make a table for the side of Cantor square in centimeter (x) and the number of squares (y), and the log-log plot of x versus y gives a straight line.

What is fractal dimension of the Cantor gasket?

Project b - Fractal dimension of the Menger sponge

The first three generations of the Menger sponge are shown here (see, Lesson 5)

You first make a table for the side in centimeter (x) and the volume in cubic centimeter (y), and again the log-log plot of x versus y gives a straight line.

What is fractal dimension of the Menger sponge?

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