Visualize 2D vector fields with arrow plots, streamlines, and magnitude coloring. Enter component functions F(x,y) and G(x,y).
Type the two component functions of a plane vector field - F(x,y) for the x-direction, G(x,y) for the y-direction - and the tool draws the field over the visible domain: an arrow at every sample point, a magnitude-based color scale, and streamlines that follow the flow. It is a drawing tool, not an equation solver: each arrow is the instantaneous vector at its own point, so the plot is a frozen snapshot of motion. The most common misreading is speed: arrow length is not always a reliable speed cue, so trust the magnitude colors - and verify direction at one point you can compute by hand.
A concrete input and expected output from the current implementation.
Input
F(x,y) = -y and G(x,y) = x
Expected output
A counterclockwise rotation field. Along the positive x-axis every arrow points straight up; along the positive y-axis, straight left; the negative axes point down and right. Arrow length and color both grow with distance from the origin, since magnitude is sqrt(x^2 + y^2): the field is weakest at the center and strongest at the view edges. The streamlines are concentric circles centered on the origin.
This is the classic rotation field: divergence 0, curl 2. A particle released anywhere orbits the origin at constant speed, and each arrow is the velocity it has at that point, so every particle path is a circle.
The tool covers the visible region with a sampling grid and evaluates F and G at each grid point. Every arrow has the direction of the vector (F, G) there and a length tied to its magnitude, while the color scale encodes the same magnitude. Where a component is undefined - division by zero, square root of a negative - no arrow appears at that point.
A streamline is an integral curve: a curve tangent to the arrow at every point it passes, so a particle released on one follows it exactly. The tool traces streamlines from seed points by stepping along the local field direction. The color scale maps sqrt(F^2 + G^2), the field magnitude, onto a ramp, which is the reliable way to compare strength between regions.
Probably because arrow size is scaled to the strongest vector currently in view, so relative sizes hold within one view but not across different zoom levels or fields. Treat the magnitude color scale as the speed readout, and check one hand-computable point. If the components are genuinely constant, the field really is uniform.
For a field that depends only on x and y, yes: the streamline is tangent to the velocity at every point, so a particle released on it stays on it. It does not show speed, though - the same circle can be traversed slowly or quickly, and only the magnitude colors reveal how fast.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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