Interactive cobweb plot with Makie

cobweb.jl

using Makie, GLMakie

f(x::Real, r::Real) = r * x * (1 - x)
function cobweb(
        xᵢ::Real,
        curve_f::Function,
        r::Real;
        nstep::Real = 30
    )::Vector{Point2f} # col 1 is x, col 2 is y

    a = zeros(nstep*2, 2)
    a[1, 1] = xᵢ
    x = xᵢ
    y = curve_f(x, r)
    ret = similar(Vector{Point2f}, nstep*2)
    ret[1] = Point2f(x, 0)
    for i ∈ 2:2:nstep*2-2
        a[i, 1] = x
        a[i, 2] = y
        x = y
        y = curve_f(x, r)
        a[i+1, 1] = x
        a[i+1, 2] = x
        ret[i] = Point2f(a[i, 1], a[i, 2])
        ret[i+1] = Point2f(a[i+1, 1], a[i+1, 2])
    end

    return ret

end


xᵢ = 0.1
rᵢ = 2.8
xr = 0:0.001:1

fig = Figure()
ax = Axis(
    fig[1, 1],
    xlabel = L"x_{n}",
    xlabelsize = 30,
    ylabel = L"x_{n+1}",
    ylabelsize = 30,
    title = "Cobweb plot",
    aspect = AxisAspect(1),
)

sg = SliderGrid(fig[2, 1],
    (label = "xᵢ", range = 0:0.01:1, startvalue = xᵢ),
    (label = "r",  range = 0:0.01:4, startvalue = rᵢ),
)

fs = lift(r -> f.(xr, r), sg.sliders[2].value)
cw = lift((x, r) -> cobweb(x, f, r), sg.sliders[1].value, sg.sliders[2].value)

lines!(ax,                # plot x=y, the bisector line
    xr,                   # xs
    xr,                   # ys
    linestyle = :dash,    # style of line
    linewidth = 3,        # width of line
    color = :blue         # colour of line
)

lines!(ax, xr, fs) # plot the curve

lines!(ax, cw) # plot the cobweb


# Set up mouse interaction

MakieLayout.deactivate_interaction!(ax, :rectanglezoom)

point = select_point(ax.scene)
on(point) do val
    set_close_to!(sg.sliders[1], val[1])
end