klein bottle

using GLMakie
GLMakie.activate!()
GLMakie.closeall() # close any open screen

# The bottle
u = LinRange(0, π, 100)
v = LinRange(0, 2π, 100)
x = [-2 / 15 * cos(u) * (3 * cos(v) - 30 * sin(u) + 90 * cos(u)^4 * sin(u)
    - 60 * cos(u)^6 * sin(u) + 5 * cos(u) * cos(v) * sin(u)) for u in u, v in v]
y = [-1 / 15 * sin(u) * (3 * cos(v) - 3 * cos(u)^2 * cos(v) - 48 * cos(u)^4 * cos(v) + 48 * cos(u)^6 * cos(v)
    - 60 * sin(u) + 5 * cos(u) * cos(v) * sin(u) - 5 * cos(u)^3 * cos(v) * sin(u)
    - 80 * cos(u)^5 * cos(v) * sin(u) + 80 * cos(u)^7 * cos(v) * sin(u)) for u in u, v in v]
z = [2 / 15 * (3 + 5 * cos(u) * sin(u)) * sin(v) for u in u, v in v]

fig = Figure(size = (1200, 800))
ax = LScene(fig[1, 1], show_axis = false)
surface!(ax, x, y, z; color = sqrt.(x.^2 .+ y.^2), colormap = (:Spectral_11, 0.8))
fig