Peano curve

A Peano curve is a special kind of mathematical figure called a space-filling curve. It’s a continuous, unbroken line that weaves back and forth in such a way that it eventually covers every point inside a square or a rectangle, effectively filling the entire space. Imagine drawing a line that starts at one corner and, without lifting your pen, traces a complex pattern that fills the whole area, leaving no gaps. This concept challenges our intuition about lines and areas, showing that a single, continuous curve can encompass an entire space, no matter how complex the pattern.