Find the dimension of the object and state whether or not it is a fractal.
-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.
A)The dimension is 2.086 and the object is fractal.
B)The dimension is 1 and the object is ordinary (non-fractal).
C)The dimension is 1.086 and the object is fractal.
D)The dimension is 0.921 and the object is fractal.

Question

Quizplus · Accepted Answer

The dimension can be calculated using the formula for fractal dimension $D = \frac{\log(N)}{\log(S)}$, where $N$ is the factor by which the number of length elements increases, and $S$ is the factor by which the length of the ruler is reduced. Substituting $N = 7$ and $S = 6$ gives $D = \frac{\log(7)}{\log(6)} \approx 1.086$, indicating that the object is a fractal.

Find the Dimension of the Object and State Whether or Not