In [fractal geometry](https://en.wikipedia.org/wiki/Fractal_geometry "Fractal geometry"), a **fractal dimension** is a ratio providing a statistical index of [complexity](https://en.wikipedia.org/wiki/Complexity "Complexity") comparing how detail in a pattern (strictly speaking, a [fractal](https://en.wikipedia.org/wiki/Fractal "Fractal") pattern) changes with the scale at which it is measured. A good example of this is the iterative process of creating a [Koch snowflake](https://en.wikipedia.org/wiki/Koch_snowflake). The Koch snowflake can be constructed by starting with an [equilateral triangle](https://en.wikipedia.org/wiki/Equilateral_triangle "Equilateral triangle"), then recursively altering each line segment as follows: 1. divide the line segment into three segments of equal length. 2. draw an equilateral triangle that has the middle segment from step 1 as its base and points outward. 3. remove the line segment that is the base of the triangle from step 2. See below for the first few steps.... ![[metrics_KochSnowFlake.png|500]] **Therefore its dimension might best be described not by its usual topological dimension of 1 (even though it is a line) but by its fractal dimension, which is often a number between one and two; in the case of the Koch snowflake, it is about 1.262.**