3D Random Walk Plot

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

Section

A random walk is built by computing the cumulative sum of random step deltas. Enum.scan(deltas, 0, fn d, acc -> acc + d end) builds the running total in Elixir. Three separate Scatter3d traces (one per walk) give each a distinct color.

alias Plotly.{Figure, Scatter3d}

:rand.seed(:exsplus, {1, 2, 3})

n = 500
step = fn -> :rand.normal() * 0.1 end

walk = fn ->
  xs = Enum.scan(1..n, 0.0, fn _, acc -> acc + step.() end)
  ys = Enum.scan(1..n, 0.0, fn _, acc -> acc + step.() end)
  zs = Enum.scan(1..n, 0.0, fn _, acc -> acc + step.() end)
  {xs, ys, zs}
end

{x1, y1, z1} = walk.()
{x2, y2, z2} = walk.()
{x3, y3, z3} = walk.()

Figure.new()
|> Figure.add_trace(Scatter3d.new(x: x1, y: y1, z: z1, mode: "lines", name: "Walk 1",
     line: %{color: "blue", width: 2}))
|> Figure.add_trace(Scatter3d.new(x: x2, y: y2, z: z2, mode: "lines", name: "Walk 2",
     line: %{color: "red", width: 2}))
|> Figure.add_trace(Scatter3d.new(x: x3, y: y3, z: z3, mode: "lines", name: "Walk 3",
     line: %{color: "green", width: 2}))
|> Figure.update_layout(
  title: "3D Random Walk",
  scene: %{
    xaxis: %{title: "X"},
    yaxis: %{title: "Y"},
    zaxis: %{title: "Z"}
  }
)
|> Plotly.show()