Space-filling curve

Let's say you have a big piece of paper and you want to color it all in, but you're not allowed to lift up your marker or go over the same spot twice. This is kind of like what a space-filling curve does, but in three dimensions instead of two.

A space-filling curve is a special type of line that winds and twists around in a way that fills up an entire space. Imagine you have a big empty room with nothing in it. A space-filling curve would be a line that starts at one wall, winds its way around the room, and eventually touches every single point in the room before coming back to where it started.

It's like a big snake that slithers around the whole room, but instead of just lying on the floor it goes up and down and even loops around itself! There are many different types of space-filling curves, and they can look really weird and wiggly, but they're all really good at filling up space without leaving any gaps.

Scientists use space-filling curves to help map out complicated shapes and volumes, because they make it easier to measure and compare different parts of the space. So even though they might seem like just a cool-looking pattern, space-filling curves are actually really useful tools in math and science!