Wind, water, magnetism — underneath, they share one simple idea. We'll build it up a piece at a time, and everything here is something you can pick up and move.
An arrow is really just two numbers: how far across, and how far up. Grab the tip and move it — watch the numbers change.
That little pair is what we call a vector. Nothing more mysterious than that.
Place an arrow at every point on a grid and you have a field. Here they all point the same way — a uniform field.
Turn the dial, and the whole field turns together.
Now the good part: make each arrow depend on where it sits. These all point toward the dot. Move it, and the whole field reorganizes.
A rule like that — one arrow for every point in space — is exactly what a vector field is.
Drop in some specks and let them follow the arrows. They drift along the very field you just built.
This is how wind maps, smoke and ocean currents are really drawn: countless tiny things, each obeying the arrow beneath it.
Here's the field you built, drawn at full scale — and rendered two ways. It's all the same arrows underneath. Drag the dot, flip toward/around, and switch the material.