Monster Curves !link!

Let that sink in.

Where $N$ is the number of self-similar pieces and $s$ is the scaling factor.

As mathematician Hans Hahn once put it: "The concept of a curve is far richer and more terrifying than anyone had imagined."

As you iterate, the "curve" gets longer and more tangled. After 1 step, it's a scribble. After 3 steps, it looks like a maze. After 10 steps, your computer screen can't tell the difference between the curve and the solid square.

By iteration 6, you'll be staring at a solid square. And you’ll know, lurking inside that square, is a monster.

In the realm of mathematics, there exist curves that defy conventional expectations, exhibiting properties that are both intriguing and counterintuitive. Among these, a special class of curves has captivated the imagination of mathematicians and scientists alike: the Monster Curves. These extraordinary curves, also known as "monstrous" or "fractal" curves, have been a subject of interest in various fields, including mathematics, physics, and computer science.