Question

In measuring the length of the object, when you reduce the length of your ruler by a factor of 6, the number of length elements increases by a factor of 7. Find the dimension of the object and state whether or not it is a fractal.

Answer #1

**SOLUTION:**

From given data,

**In measuring
the length of the object, when you reduce the length of your ruler
by a factor of 6, the number of length elements increases by a
factor of 7. Find the dimension of the object and state whether or
not it is a fractal.**

The length of your ruler by a factor =R = 6

The number of length elements increases by a factor = N= 7

From the definition of fractal dimensions.

N = R^{D}

Therefore,

7 = 6^{D}

Applying ln on both sides

ln 7 =ln 6^{D}

ln 7 = D ln 6

D = ln 7 / ln 6

D = 1.086

The dimension of the object is found to be 1.086 unit and hence it is a fractal.

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