makie_carrot_growth.jl

growth(🐇, 🥕) = 🐇 * 🥕 * (1.0 - 🐇)
function orbitdiagram(growth, r1, r2, n = 500, a = zeros(1000, n); T = 1000)
    rs = range(r1, stop = r2, length = 1000)
    for (j, r) in enumerate(rs)
        x = 0.5
        for _ in 1:T; x = growth(x, r); end
        for i in 1:n
            x = growth(x, r)
            @inbounds a[j, i] = x
        end
    end
    rs, a
end
r1 = slider(0:0.001:4, raw = true)
r2 = slider(0:0.001:4, raw = true)
n1 = 500; n2 = 1000; a = zeros(n2, n1)
positions = Vector{Point2f0}(undef, n1 * n2)
pos = lift(r1[end][:value], r2[end][:value]) do r1, r2
    global a
    rs, a = orbitdiagram(growth, r1, r2, size(a, 2), a)
    dim = size(a, 2)
    for (i, r) in enumerate(rs)
        positions[((i-1)*dim) + 1 : (i*dim)] .= Point2f0.(r, view(a, i, :))
    end
    positions
end
p = scatter(pos, markersize = 0.005, color = (:black, 0.4),limits = FRect3D(Vec3f0(0, 0, 0), Vec3f0(4, 1, 0)))
scene = hbox(
    p,
    vbox(r1, r2)
)
scene