Find the dimension of the object and state whether or not it is a fractal.
-In measuring the volume of the object, when you reduce the length of your ruler by a factor of 5, the number of length elements increases by a factor of 60.
A)The dimension is 55 and the object is ordinary (non-fractal).
B)The dimension is 2.544 and the object is fractal.
C)The dimension is 0.393 and the object is fractal.
D)The dimension is 3.544 and the object is fractal.

Question

Quizplus · Accepted Answer

The dimension can be found 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 scale factor by which the ruler length is reduced. Here, $N = 60$ and $S = 5$, so $D = \frac{\log(60)}{\log(5)} \approx 2.544$. Since the dimension is not an integer, the object is a fractal.

Find the Dimension of the Object and State Whether or Not