Fractals also have a dimension associated with them. It is in no way similar to Euclidean dimension. Fractal dimension is a measure of the degree of roughness or fragmentation of an object. The dimension of a fractal can be a fraction. The greater a figure's dimension, the greater it's complexity.
All fractals have some pattern that repeats itself infinitely.
The creation of a fractal results from the iteration of the steps that create the repetitive pattern within the object. Generator iteration creates base-motif fractals. This type of iteration repeatedly replaces a component of the original shape with another shape. The original shape is called the base, and the pattern used to replace the base is called the motif. Generator iteration creates dusts, clusters, curves, sweeps, and l-systems.