Explanation Given: In measuring the length of the object, when the length of the ruler is reduced by a factor of 2 the number of volume elements increases by a factor of 8. Formula used: Fractal dimension D of the object is found from N=R D Where, N is the factor by which number of element increases when ruler is shortened by a factor R. Taking logarithm on both the sides- log(N)=log(R D ) log(N)=D log(R) [applying the rule log(a x )=x log(a) to right hand side] D = log ( N ) log ( R ) An object is defined as fractal if it has a non-integer dimension...

Using and Understanding Mathematics: A Quantitative Reasoning Approach plus NEW MyMathLab with Pearson eText -- Access Card Package (6th Edition) (Bennett Science & Math Titles)

6th Edition

ISBN: 9780321923219

Author: Jeffrey O. Bennett, William L. Briggs

Publisher: PEARSON

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Chapter 10.C, Problem 17E

To determine

The dimension of an object and state whether or not it is a fractal, given that in measuring the length of the object, when the length of the ruler is reduced by a factor of 2 the number of volume elements increases by a factor of 8.

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Chapter 10.C, Problem 16E

Chapter 10.C, Problem 18E

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Using and Understanding Mathematics: A Quantitative Reasoning Approach plus NEW MyMathLab with Pearson eText -- Access Card Package (6th Edition) (Bennett Science & Math Titles)

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