julia-lorenz.jl

using ODE, Plots

function lorenz(t, r)
  # Extract the coordinates from the r vector
  (x, y, z) = r

  # The Lorenz equations
  dx_dt = σ*(y - x)
  dy_dt = x*(ρ - z) - y
  dz_dt = x*y - β*z

  # Return the derivatives as a vector
  [dx_dt; dy_dt; dz_dt]
end

const σ = 10.0
const ρ = 28.0
const β = 8.0/3.0

(t, pos) = ode45(lorenz, [0.1; 0.0; 0.0], 0:0.001:50)

x = map(v->v[1], pos)
y = map(v->v[2], pos)
z = map(v->v[3], pos)

plot3d(x, y, z)

ENV["PLOTS_TEST"] = "true"  # using test mode

jump = 10

anim = @animate for i in 1:cld(length(pos), jump)
    i = 1 + (i-1)*jump
    plot3d(x[1:i], y[1:i], z[1:i], xlim=(-25,25), ylim=(-25,25), zlim=(0,50),
    　　　　title = "Lorenz Attractor", label="")
end

gif(anim, "lorenz.gif", fps = 15)