Find the dimension of the object and state whether or not it is a fractal.
-In measuring the area of the object, when you reduce the length of your ruler by a factor of 3, the number of length elements increases by a factor of 12.
A)The dimension is 0.442 and the object is fractal.
B)The dimension is 9 and the object is ordinary (non-fractal).
C)The dimension is 2.262 and the object is fractal.
D)The dimension is 3.262 and the object is fractal.

Question

Quizplus · Accepted Answer

The dimension of the object 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 length is reduced. Here, $N = 12$ and $S = 3$, so $D = \frac{\log(12)}{\log(3)} = 2.262$. Since the dimension is not an integer and greater than 1, the object is a fractal.

Find the Dimension of the Object and State Whether or Not