In mathematics, the Menger sponge is a fractal curve.

"With subsequent drawings of the fractal curve, sudden changes may appear."

"Details emerge more clearly as the fractal curve is redrawn."

Their lights flowed upward in a fractal curve of luminance.

(A general exploration of the modular group symmetry in fractal curves.)

These features are evident in the two examples of fractal curves.

But we cannot do either of these things, because fractal curves have complexity in the form of self-similarity and detail that ordinary lines lack.

Squares can be used to generate similar fractal curves.

It's sort of a fractal curve of new markets living within markets.

One such fractal curve with an infinite perimeter and finite surface area is the Koch snowflake.