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.
A fractal is a shape which is made up of parts similar to the whole in some way.
A second definitive characteristic of fractals is the dimensional realm in which they exist.
Fractals have dimensions in between 1 and 2, and in between 2 and 3.
A fractal is a recursively created never-ending pattern that is usually self-similar in nature.
Separate from Euclidean geometry, fractal geometry addresses the more non-uniform shapes found in nature, such as mountains, clouds and trees.
Fractals provide a systematic method to capture the “roughness” of some objects.