 # Can a fractal dimension be less than 1?

## Can a fractal dimension be less than 1?

The simplest example of a fractal structure with dimension less than one is the Cantor set. Ones starts with the unit interval [0,1], then delete the middle third of the segment, then what remains are two closed segments: [0,1/3] and [2/3,1], where each has length 1/3.

### Can Fractals be measured?

A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale. Several types of fractal dimension can be measured theoretically and empirically (see Fig. 2).

What is mass fractal dimension?

The expression which embodies the whole concept of the fractal structure of aggregates is very simple:(1) M∝R D f where M is the mass of particles, R is a linear measure of size and Df is the mass fractal dimension, which is a measure of the scaling and degree of rugosity of the structure.

How do you calculate fractals?

D = log N/log S. This is the formula to use for computing the fractal dimension of any strictly self-similar fractals. The dimension is a measure of how completely these fractals embed themselves into normal Euclidean space.

## How do you describe fractal dimension?

Fractal dimension is a measure of how “complicated” a self-similar figure is. In a rough sense, it measures “how many points” lie in a given set. A plane is “larger” than a line, while S sits somewhere in between these two sets.

### What is the maximum dimension a fractal can have?

RESULTS AND DISCUSSION. The FD dynamic ranges were variable according to the algorithm used. The morphological (FDM) and the pore mass fractal (FDMF) methods presented the highest dynamic ranges of fractal dimension: [1.939, 2.426] and [2.523, 3.754].

Is golden ratio a fractal?

The Fibonacci Spiral, which is my key aesthetic focus of this project, is a simple logarithmic spiral based upon Fibonacci numbers, and the golden ratio, Φ. Because this spiral is logarithmic, the curve appears the same at every scale, and can thus be considered fractal.

Are our lungs fractals?

The lungs are an excellent example of a natural fractal organ. If you look at the tree upside-down (mouse over the image), you can see that the lungs share the same branching pattern as the trees. And it is for good reason! Both the trees and lungs have evolved to serve a similar function – respiration.