A fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal.[1] In general, fractal curves are nowhere rectifiable curves — that is, they do not have finite length — and every subarc longer than a single point has infinite length.[2]
A famous example is the boundary of the Mandelbrot set.
- ^ "Geometric and topological recreations".
- ^ Ritzenthaler, Chella. "Fractal Curves" (PDF).