What are power-law relationships?

Power-law relationships are when one thing changes in a special way as another thing grows or shrinks.

Imagine you have a bag of marbles. If you double the number of marbles in your bag, and the size of each marble stays the same, then the total size of all the marbles also doubles. But with power-law relationships, it’s not always that simple. Sometimes, if you double the size of something, like a picture on your phone, the amount of memory it takes up doesn’t just double. It might grow much faster or slower.

Think about climbing stairs. If you go from one step to another, you’re making small changes. But if you're going from the first floor all the way to the top, that’s a big change, and it feels like it takes more effort. Power-law relationships are kind of like that: small changes can lead to big differences, or big changes might not feel as huge.

When you zoom in on a map, if you make it twice as big, the area you see becomes four times bigger, because both length and width grow by two. That’s also a power-law relationship!

So power-law relationships are all around us, just waiting to be noticed!