Quiver Over a Contour Plot

Mix.install([
  {:plotly_ex, "~> 0.3"},
  {:kino, "~> 0.18"}
])

Overlay the gradient of a potential

The potential is z = x² + y²; its gradient is (2x, 2y). Both traces share the same Cartesian axes. The contour shows potential values, while arrows show the gradient direction and relative magnitude.

alias Plotly.{Contour, Figure, Quiver}

axis = Enum.to_list(-3..3)
positions = for x <- axis, y <- axis, do: {x, y}

Figure.new()
|> Figure.add_trace(Contour.new(
  x: axis, y: axis, z: for(y <- axis, do: for(x <- axis, do: x * x + y * y)),
  colorscale: "Blues", showscale: false
))
|> Figure.add_trace(Quiver.new(
  x: Enum.map(positions, &elem(&1, 0)), y: Enum.map(positions, &elem(&1, 1)),
  u: Enum.map(positions, fn {x, _y} -> 2 * x end),
  v: Enum.map(positions, fn {_x, y} -> 2 * y end),
  lengthmode: "raw", lengthfactor: 0.1, marker: %{color: "darkred"}, name: "Gradient"
))
|> Figure.update_layout(title: "Potential and gradient", yaxis: %{scaleanchor: "x"})
|> Plotly.show()