Being a language, mathematics may be used not only to inform but also, among other things, to seduce. Benoît B. Mandelbrot
Fractal From Latin, fractus. Broken, shattered.
A rectifiable curve
Four iterations of a Peano's curve construction, whose limit is a space-filling curve.
Four iterations of the Koch snowflake. This fractal is strongly self-similar.
If you are fond of pictures and nice animations, you can watch this wonderful video by 3Blue1Brown on the same topic (more or less).