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In measuring the length of the object, when you reduce the length of your ruler by...

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.

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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 = RD

Therefore,

7 = 6D

Applying ln on both sides

ln 7 =ln 6D

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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