Vector Field Streamplot

Visualisation of vector fields and their streamlines

The flow of 2D dynamical systems can be visualised by plotting streamlines of vector fields defined by the differential equations:

\[\frac{dx}{dt} = f(x, y)\] \[\frac{dy}{dt} = g(x, y)\] 

{
  "data": [],
  "layout": {
    "title": "Vector Field Streamplot",
    "xaxis": {"title": "x", "range": [-3, 3], "zeroline": true, "zerolinecolor": "#666", "zerolinewidth": 1},
    "yaxis": {"title": "y", "range": [-3, 3], "zeroline": true, "zerolinecolor": "#666", "zerolinewidth": 1},
    "margin": {"l": 50, "r": 50, "b": 50, "t": 50},
    "showlegend": false,
    "plot_bgcolor": "rgba(0,0,0,0)",
    "paper_bgcolor": "rgba(0,0,0,0)"
  }
}
Differential Equations
Use x, y, sin(), cos(), exp(), log(), sqrt(), pow()
Use x, y, sin(), cos(), exp(), log(), sqrt(), pow()
to
to
Unbroken lines that flow smoothly across the domain
Display vector field direction indicators
Example Systems

About Vector Field Streamplots

A streamplot visualizes the flow of a 2D dynamical system by showing 'streamlines' that are tangent to the vector field at every point. Each streamline represents a possible trajectory that a particle would follow if placed in the field.

Supported Functions:

You can use standard mathematical functions in your equations: sin(), cos(), tan(), exp(), log(), sqrt(), pow(), abs(), and basic arithmetic operations (+, -, *, /, ^).

Interpreting the Plot:

  • Streamlines: Show the direction and path of flow at different points
  • Arrows: Indicate the local direction of the vector field
  • Fixed Points: Look for regions where streamlines converge or diverge
  • Periodic Orbits: Closed loops in the streamlines indicate oscillatory behavior