  Using the moving frame and invariants, any discrete curve in $\R^3$ could be
uniquely identified by its centroaffine curvatures and torsions. In this paper,
depending on the affine curvatures of the fractal curves, such as Koch curve
and Hilbert curve, we can clearly describe their iterative regularities.
Interestingly, by the affine curvatures, the fractal curves can be quantified
and encoded accordingly to a sequence. Hence, it is more convenient for future
reference. Given three starting points, we can directly generate the affine
Koch curve and affine Hilbert curve at the step $n, \forall n\in \mathbb{Z}^+$.
Certainly, if the initial three points are standard, the curve is the
traditional Koch curve or Hilbert curve. By this method, the characteristic of
some fractal curves which look like irregular could be quantified, and the
regularities would become more obvious.
