Iron filings, a weather map, a leaf on a stream. Drop particles into a field, then measure how much it spreads and how much it spins.
The blob is a ring of particles carried by the flow. Watch whether it grows, shrinks, or turns.
Drag the probe anywhere to measure; switch fields to compare.
A vector field attaches an arrow to every point of the plane. The single most common mistake is to draw all those arrows starting at the origin — each arrow lives at its own point, and it says what happens to something sitting exactly there.
The drifting dots make that concrete. Each one just reads the arrow underneath it and moves that way. Iron filings, a weather map, a leaf on a stream.
The blob is where the two derived quantities come from. Drop a small circle of particles into the flow and let it go. If it grows, the field has positive divergence there — the flow is spreading out, and something must be pouring in. If it turns, the field has nonzero curl — the flow is rotating, which is what the little paddlewheel measures.
Try the swirl: it turns hard but never changes size, so it has curl and no divergence. The source is the opposite — it grows without turning. The shear field looks like it does nothing interesting, and yet the blob quietly rotates: shear carries curl too, which is exactly the fact that makes curl worth defining.