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 3 the number of length elements increases by a factor of 27.
A)The dimension is 1 and the object is ordinary (non-fractal).
B)The dimension is 2 and the object is ordinary (non-fractal).
C)The dimension is 3 and the object is a fractal.
D)The dimension is 3 and the object is ordinary (non-fractal).

Question

Quizplus · Accepted Answer

The dimension is 3 because when the ruler is reduced by a factor of 3, the number of length elements increases by a factor of 27, which is $3^3$. This indicates a three-dimensional object. The object is ordinary (non-fractal) because this scaling behavior is consistent with classical, Euclidean geometry, not fractal geometry.

Find the Dimension of the Object and State Whether or Not